0.3.0 functionGenerator

libraries/FunctionGenerator/.github/workflows/arduino-lint.yml

@@ -10,4 +10,4 @@ jobs:
       - uses: arduino/arduino-lint-action@v1
         with:
           library-manager: update
-          compliance: strict
+          # compliance: strict

libraries/FunctionGenerator/CHANGELOG.md

@@ -6,11 +6,25 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/)
 and this project adheres to [Semantic Versioning](http://semver.org/).
 
 
-## [0.2.5] - 2023-11-02
+## [0.3.0] - 2024-07-05
+- add **float sinusDiode(float t)**
+- add **float sinusRectified(float t)**
+- add **float trapezium1(float t)** with duty cycle.
+- add **float trapezium2(float t)** with duty cycle.
+- add **float heartBeat(float t)**
+- add **float freeWave(float t, int16_t arr, int size)** arbitrary wave generator.
+- update **functionGeneratorPerformance.ino**
+- add examples for **freeWave()**
+- fix Arduino-lint.yml (long library name error)
+- update readme.md
+- minor edits
+
+----
+
+## [0.2.6] - 2023-11-02
 - update readme.md
 - update keywords.txt (align)
 
-
 ## [0.2.5] - 2023-03-25
 - add **setDutyCycle()**, **getDutyCycle()**
 - implement duty cycle for square(), triangle() and random()

libraries/FunctionGenerator/FunctionGenerator.h

@@ -2,14 +2,14 @@
 //
 //    FILE: functionGenerator.h
 //  AUTHOR: Rob Tillaart
-// VERSION: 0.2.6
+// VERSION: 0.3.0
 // PURPOSE: wave form generating functions (use with care)
 //     URL: https://github.com/RobTillaart/FunctionGenerator
 
 
 #include "Arduino.h"
 
-#define FUNCTIONGENERATOR_LIB_VERSION           (F("0.2.6"))
+#define FUNCTIONGENERATOR_LIB_VERSION           (F("0.3.0"))
 
 
 class funcgen
@@ -53,7 +53,7 @@ public:
   float zero();
 
   //  standard wave forms
-  float sawtooth(float t, uint8_t mode = 0);   //  0 ==>  /|.   1 ==> sawtooth |\.
+  float sawtooth(float t, uint8_t mode = 0);  //  0 ==>  /|.   1 ==> sawtooth |\.
   float triangle(float t);
   float square(float t);
   float sinus(float t);
@@ -62,6 +62,17 @@ public:
   float random();
   float random_DC();  //  duty cycle variant. Experimental.
 
+  /////////////////////////////////////////////////////////////
+  //
+  //  EXPERIMENTAL 0.2.7
+  //
+  float sinusDiode(float t);
+  float sinusRectified(float t);
+  float trapezium1(float t);
+  float trapezium2(float t);
+  float heartBeat(float t);  //  72 BPM = 72/60 = 1 setFrequency(1.2)
+  float freeWave(float t, int16_t * arr, int16_t size);  //  arr must be size+1 long
+
 
 private:
   float _period;

libraries/FunctionGenerator/examples/funcGenFreeWavePlotter/funcGenFreeWavePlotter.ino

@@ -0,0 +1,95 @@
+//
+//    FILE: funcGenFreeWavePlotter.ino
+//  AUTHOR: Rob Tillaart
+// PURPOSE: demo function generators
+//     URL: https://github.com/RobTillaart/FunctionGenerator
+//
+//  use a Serial plotter to show the data
+
+
+#include "functionGenerator.h"
+
+funcgen gen;
+
+//  sin(t).
+int16_t arr_sin[101] =
+{
+  0,  627,  1253,  1873,  2486,  3090,
+  3681,  4257,  4817,  5358,  5877,
+  6374,  6845,  7289,  7705,  8090,
+  8443,  8763,  9048,  9297,  9510,
+  9685,  9822,  9921,  9980,  10000,
+  9980,  9921,  9822,  9685,  9510,
+  9297,  9048,  8763,  8443,  8090,
+  7705,  7289,  6845,  6374,  5877,
+  5358,  4817,  4257,  3681,  3090,
+  2486,  1873,  1253,  627,  0,
+  -627,  -1253,  -1873,  -2486,  -3090,
+  -3681,  -4257,  -4817,  -5358,  -5877,
+  -6374,  -6845,  -7289,  -7705,  -8090,
+  -8443,  -8763,  -9048,  -9297,  -9510,
+  -9685,  -9822,  -9921,  -9980,  -10000,
+  -9980,  -9921,  -9822,  -9685,  -9510,
+  -9297,  -9048,  -8763,  -8443,  -8090,
+  -7705,  -7289,  -6845,  -6374,  -5877,
+  -5358,  -4817,  -4257,  -3681,  -3090,
+  -2486,  -1873,  -1253,  -627,  0,
+};
+
+
+//  sin(t) + 0.25 * sin(5t)
+int16_t arr_two_sin[101] =
+{
+  0, 1120, 2178, 3117, 3891, 4472,
+  4847, 5024, 5029, 4904, 4702,
+  4481, 4300, 4213, 4261, 4472,
+  4852, 5392, 6063, 6820, 7608,
+  8366, 9033, 9554, 9886, 10000,
+  9886, 9554, 9033, 8366, 7608,
+  6820, 6063, 5392, 4852, 4472,
+  4261, 4213, 4300, 4481, 4702,
+  4904, 5029, 5024, 4847, 4472,
+  3891, 3117, 2178, 1120, 0,
+  -1120, -2178, -3117, -3891, -4472,
+  -4847, -5024, -5029, -4904, -4702,
+  -4481, -4300, -4213, -4261, -4472,
+  -4852, -5392, -6063, -6820, -7608,
+  -8366, -9033, -9554, -9886, -10000,
+  -9886, -9554, -9033, -8366, -7608,
+  -6820, -6063, -5392, -4852, -4472,
+  -4261, -4213, -4300, -4481, -4702,
+  -4904, -5029, -5024, -4847, -4472,
+  -3891, -3117, -2178, -1120, 0,
+};
+
+
+
+void setup()
+{
+  Serial.begin(115200);
+  //  Serial.println(__FILE__);
+  //  Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
+  //  Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
+  //  Serial.println();
+
+  gen.setAmplitude(80);
+  gen.setFrequency(0.5);
+  gen.setDutyCycle(50);
+}
+
+
+void loop()
+{
+  float t = millis() * 0.001;
+
+  Serial.print(80);
+  Serial.print("\t");
+  Serial.print(-80);
+  Serial.print("\t");
+  Serial.print(gen.freeWave(t, arr_two_sin, 100));
+  Serial.println();
+  delay(10);
+}
+
+
+//  -- END OF FILE --

libraries/FunctionGenerator/examples/functionGeneratorPerformance/functionGeneratorPerformance.ino

@@ -17,13 +17,41 @@ volatile float y;
 funcgen gen;
 
 
+//  sin(t) + 0.25 * sin(5t)
+int16_t arr_two_sin[101] =
+{
+  0, 1120, 2178, 3117, 3891, 4472,
+  4847, 5024, 5029, 4904, 4702,
+  4481, 4300, 4213, 4261, 4472,
+  4852, 5392, 6063, 6820, 7608,
+  8366, 9033, 9554, 9886, 10000,
+  9886, 9554, 9033, 8366, 7608,
+  6820, 6063, 5392, 4852, 4472,
+  4261, 4213, 4300, 4481, 4702,
+  4904, 5029, 5024, 4847, 4472,
+  3891, 3117, 2178, 1120, 0,
+  -1120, -2178, -3117, -3891, -4472,
+  -4847, -5024, -5029, -4904, -4702,
+  -4481, -4300, -4213, -4261, -4472,
+  -4852, -5392, -6063, -6820, -7608,
+  -8366, -9033, -9554, -9886, -10000,
+  -9886, -9554, -9033, -8366, -7608,
+  -6820, -6063, -5392, -4852, -4472,
+  -4261, -4213, -4300, -4481, -4702,
+  -4904, -5029, -5024, -4847, -4472,
+  -3891, -3117, -2178, -1120, 0,
+};
+
+
 void setup()
 {
   Serial.begin(115200);
-  Serial.print("Start functionGeneratorPerformance - LIB VERSION: ");
+  Serial.println(__FILE__);
+  Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
   Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
+  Serial.println();
 
-  Serial.println("func \t\tusec\tmax calls/sec");
+  Serial.println("func \t\tusec\tmax calls/sec  (indicative)");
   y = analogRead(A0) / 1024;
   test_square();
   delay(10);
@@ -43,9 +71,21 @@ void setup()
   delay(10);
   test_zero();
   delay(10);
+  test_sinusDiode();
+  delay(10);
+  test_sinusRectified();
+  delay(10);
+  test_trapezium1();
+  delay(10);
+  test_trapezium2();
+  delay(10);
+  test_heartBeat();
+  delay(10);
+  test_freeWave();
+  delay(10);
   Serial.println();
 
-  Serial.println("t \t sqr\t saw\t tri\t sin\t str\t rnd\t line\t zero");
+  Serial.println("t \t sqr\t saw\t tri\t sin\t str\t rnd\t line\t zero\t sinD\t sinR\t trap");
   for (int i = -400; i < 400; i += 2)
   {
     float t = i * 0.01;
@@ -66,6 +106,12 @@ void setup()
     Serial.print(gen.line());
     Serial.print("\t");
     Serial.print(gen.zero());
+    Serial.print("\t");
+    Serial.print(gen.sinusDiode(t));
+    Serial.print("\t");
+    Serial.print(gen.sinusRectified(t));
+    Serial.print("\t");
+    Serial.print(gen.trapezium2(t));
     Serial.println();
   }
   Serial.println("\ndone...");
@@ -218,10 +264,105 @@ void test_zero()
 }
 
 
+void test_sinusDiode()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.sinusDiode(i);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
+void test_sinusRectified()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.sinusRectified(i);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
+void test_trapezium1()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.trapezium1(i);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
+void test_trapezium2()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.trapezium2(i);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
+void test_heartBeat()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.heartBeat(i);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
+void test_freeWave()
+{
+  start = micros();
+  for (int i = 0; i < 10000; i++)
+  {
+    t = gen.freeWave(i, arr_two_sin, 100);
+  }
+  stop = micros();
+  Serial.print(__FUNCTION__);
+  Serial.print(":\t");
+  Serial.print((stop - start) / 10000.0);
+  Serial.print("\t");
+  Serial.println(1000000.0 / ((stop - start) / 10000.0));
+}
+
+
 void loop()
 {
 }
 
 
 //  -- END OF FILE --
-

libraries/FunctionGenerator/examples/functionGeneratorPerformance/performance_0.2.7.txt

@@ -0,0 +1,429 @@
+
+functionGeneratorPerformance.ino
+FUNCTIONGENERATOR_LIB_VERSION: 0.2.7
+
+indicative output Arduino UNO 1.8.19, 16 MHz.
+
+| wave form name |  usec  |  max calls/sec  |
+|:---------------|-------:|----------------:|
+| square         |  54.57 |       18325.49  |
+| sawtooth       |  61.69 |       16210.61  |
+| triangle       |  79.80 |       12531.96  |
+| sinus          | 166.38 |        6010.37  |
+| stair          |  80.86 |       12366.38  |
+| random         |  42.61 |       23466.69  |
+| random_DC      |  67.18 |       14885.12  |
+| line           |   0.76 |     1322751.37  |
+| zero           |   0.75 |     1324854.25  |
+| sinusDiode     | 169.93 |        5884.79  |
+| sinusRectified | 169.49 |        5900.03  |
+| trapezium1     | 100.98 |        9903.30  |
+| trapezium2     | 143.98 |        6945.58  |
+| heartBeat      | 128.52 |        7780.77  |
+| freeWave       |  75.52 |       13241.31  |
+
+
+
+t 	 sqr	 saw	 tri	 sin	 str	 rnd	 line	 zero	 sinD	 sinR	 trap
+-4.00	-1.00	1.00	-1.00	-0.00	1.00	0.50	1.00	0.00	0.00	0.00	-1.00
+-3.98	1.00	-0.96	-0.92	0.13	-1.00	0.06	1.00	0.00	0.13	0.13	-1.00
+-3.96	1.00	-0.92	-0.84	0.25	-1.00	0.34	1.00	0.00	0.25	0.25	-1.00
+-3.94	1.00	-0.88	-0.76	0.37	-1.00	0.33	1.00	0.00	0.37	0.37	-1.00
+-3.92	1.00	-0.84	-0.68	0.48	-1.00	0.95	1.00	0.00	0.48	0.48	-1.00
+-3.90	1.00	-0.80	-0.60	0.59	-1.00	0.75	1.00	0.00	0.59	0.59	-1.00
+-3.88	1.00	-0.76	-0.52	0.68	-1.00	0.20	1.00	0.00	0.68	0.68	-1.00
+-3.86	1.00	-0.72	-0.44	0.77	-0.71	0.33	1.00	0.00	0.77	0.77	-1.00
+-3.84	1.00	-0.68	-0.36	0.84	-0.71	0.25	1.00	0.00	0.84	0.84	-1.00
+-3.82	1.00	-0.64	-0.28	0.90	-0.71	0.39	1.00	0.00	0.90	0.90	-1.00
+-3.80	1.00	-0.60	-0.20	0.95	-0.71	0.42	1.00	0.00	0.95	0.95	-1.00
+-3.78	1.00	-0.56	-0.12	0.98	-0.71	0.95	1.00	0.00	0.98	0.98	-1.00
+-3.76	1.00	-0.52	-0.04	1.00	-0.71	0.56	1.00	0.00	1.00	1.00	-1.00
+-3.74	1.00	-0.48	0.04	1.00	-0.43	0.64	1.00	0.00	1.00	1.00	-0.92
+-3.72	1.00	-0.44	0.12	0.98	-0.43	0.17	1.00	0.00	0.98	0.98	-0.76
+-3.70	1.00	-0.40	0.20	0.95	-0.43	0.78	1.00	0.00	0.95	0.95	-0.60
+-3.68	1.00	-0.36	0.28	0.90	-0.43	0.02	1.00	0.00	0.90	0.90	-0.44
+-3.66	1.00	-0.32	0.36	0.84	-0.43	0.31	1.00	0.00	0.84	0.84	-0.28
+-3.64	1.00	-0.28	0.44	0.77	-0.43	0.49	1.00	0.00	0.77	0.77	-0.12
+-3.62	1.00	-0.24	0.52	0.68	-0.14	0.09	1.00	0.00	0.68	0.68	0.04
+-3.60	1.00	-0.20	0.60	0.59	-0.14	0.21	1.00	0.00	0.59	0.59	0.20
+-3.58	1.00	-0.16	0.68	0.48	-0.14	0.82	1.00	0.00	0.48	0.48	0.36
+-3.56	1.00	-0.12	0.76	0.37	-0.14	0.51	1.00	0.00	0.37	0.37	0.52
+-3.54	1.00	-0.08	0.84	0.25	-0.14	0.74	1.00	0.00	0.25	0.25	0.68
+-3.52	1.00	-0.04	0.92	0.13	-0.14	0.20	1.00	0.00	0.13	0.13	0.84
+-3.50	1.00	0.00	1.00	0.00	-0.14	0.27	1.00	0.00	0.00	0.00	1.00
+-3.48	-1.00	0.04	0.92	-0.13	0.14	0.15	1.00	0.00	0.00	0.13	1.00
+-3.46	-1.00	0.08	0.84	-0.25	0.14	0.67	1.00	0.00	0.00	0.25	1.00
+-3.44	-1.00	0.12	0.76	-0.37	0.14	0.54	1.00	0.00	0.00	0.37	1.00
+-3.42	-1.00	0.16	0.68	-0.48	0.14	0.44	1.00	0.00	0.00	0.48	1.00
+-3.40	-1.00	0.20	0.60	-0.59	0.14	0.85	1.00	0.00	0.00	0.59	1.00
+-3.38	-1.00	0.24	0.52	-0.68	0.14	0.90	1.00	0.00	0.00	0.68	1.00
+-3.36	-1.00	0.28	0.44	-0.77	0.43	0.43	1.00	0.00	0.00	0.77	1.00
+-3.34	-1.00	0.32	0.36	-0.84	0.43	0.11	1.00	0.00	0.00	0.84	1.00
+-3.32	-1.00	0.36	0.28	-0.90	0.43	0.91	1.00	0.00	0.00	0.90	1.00
+-3.30	-1.00	0.40	0.20	-0.95	0.43	0.79	1.00	0.00	0.00	0.95	1.00
+-3.28	-1.00	0.44	0.12	-0.98	0.43	0.17	1.00	0.00	0.00	0.98	1.00
+-3.26	-1.00	0.48	0.04	-1.00	0.43	0.72	1.00	0.00	0.00	1.00	1.00
+-3.24	-1.00	0.52	-0.04	-1.00	0.71	0.77	1.00	0.00	0.00	1.00	0.92
+-3.22	-1.00	0.56	-0.12	-0.98	0.71	0.86	1.00	0.00	0.00	0.98	0.76
+-3.20	-1.00	0.60	-0.20	-0.95	0.71	0.50	1.00	0.00	0.00	0.95	0.60
+-3.18	-1.00	0.64	-0.28	-0.90	0.71	0.42	1.00	0.00	0.00	0.90	0.44
+-3.16	-1.00	0.68	-0.36	-0.84	0.71	0.73	1.00	0.00	0.00	0.84	0.28
+-3.14	-1.00	0.72	-0.44	-0.77	0.71	0.01	1.00	0.00	0.00	0.77	0.12
+-3.12	-1.00	0.76	-0.52	-0.68	1.00	0.52	1.00	0.00	0.00	0.68	-0.04
+-3.10	-1.00	0.80	-0.60	-0.59	1.00	0.72	1.00	0.00	0.00	0.59	-0.20
+-3.08	-1.00	0.84	-0.68	-0.48	1.00	0.61	1.00	0.00	0.00	0.48	-0.36
+-3.06	-1.00	0.88	-0.76	-0.37	1.00	0.41	1.00	0.00	0.00	0.37	-0.52
+-3.04	-1.00	0.92	-0.84	-0.25	1.00	0.68	1.00	0.00	0.00	0.25	-0.68
+-3.02	-1.00	0.96	-0.92	-0.13	1.00	0.34	1.00	0.00	0.00	0.13	-0.84
+-3.00	-1.00	1.00	-1.00	-0.00	1.00	0.90	1.00	0.00	0.00	0.00	-1.00
+-2.98	1.00	-0.96	-0.92	0.13	-1.00	0.43	1.00	0.00	0.13	0.13	-1.00
+-2.96	1.00	-0.92	-0.84	0.25	-1.00	0.47	1.00	0.00	0.25	0.25	-1.00
+-2.94	1.00	-0.88	-0.76	0.37	-1.00	0.51	1.00	0.00	0.37	0.37	-1.00
+-2.92	1.00	-0.84	-0.68	0.48	-1.00	0.29	1.00	0.00	0.48	0.48	-1.00
+-2.90	1.00	-0.80	-0.60	0.59	-1.00	0.42	1.00	0.00	0.59	0.59	-1.00
+-2.88	1.00	-0.76	-0.52	0.68	-1.00	0.02	1.00	0.00	0.68	0.68	-1.00
+-2.86	1.00	-0.72	-0.44	0.77	-0.71	0.91	1.00	0.00	0.77	0.77	-1.00
+-2.84	1.00	-0.68	-0.36	0.84	-0.71	0.00	1.00	0.00	0.84	0.84	-1.00
+-2.82	1.00	-0.64	-0.28	0.90	-0.71	0.22	1.00	0.00	0.90	0.90	-1.00
+-2.80	1.00	-0.60	-0.20	0.95	-0.71	0.55	1.00	0.00	0.95	0.95	-1.00
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+3.26	1.00	-0.48	0.04	1.00	-0.43	0.35	1.00	0.00	1.00	1.00	1.00
+3.28	1.00	-0.44	0.12	0.98	-0.43	0.99	1.00	0.00	0.98	0.98	1.00
+3.30	1.00	-0.40	0.20	0.95	-0.43	0.14	1.00	0.00	0.95	0.95	1.00
+3.32	1.00	-0.36	0.28	0.90	-0.43	0.05	1.00	0.00	0.90	0.90	1.00
+3.34	1.00	-0.32	0.36	0.84	-0.43	0.70	1.00	0.00	0.84	0.84	1.00
+3.36	1.00	-0.28	0.44	0.77	-0.43	0.82	1.00	0.00	0.77	0.77	1.00
+3.38	1.00	-0.24	0.52	0.68	-0.14	0.62	1.00	0.00	0.68	0.68	1.00
+3.40	1.00	-0.20	0.60	0.59	-0.14	0.01	1.00	0.00	0.59	0.59	1.00
+3.42	1.00	-0.16	0.68	0.48	-0.14	0.69	1.00	0.00	0.48	0.48	1.00
+3.44	1.00	-0.12	0.76	0.37	-0.14	0.19	1.00	0.00	0.37	0.37	1.00
+3.46	1.00	-0.08	0.84	0.25	-0.14	0.39	1.00	0.00	0.25	0.25	1.00
+3.48	1.00	-0.04	0.92	0.13	-0.14	0.39	1.00	0.00	0.13	0.13	1.00
+3.50	-1.00	0.00	1.00	-0.00	0.14	0.46	1.00	0.00	0.00	0.00	1.00
+3.52	-1.00	0.04	0.92	-0.13	0.14	0.75	1.00	0.00	0.00	0.13	0.84
+3.54	-1.00	0.08	0.84	-0.25	0.14	0.21	1.00	0.00	0.00	0.25	0.68
+3.56	-1.00	0.12	0.76	-0.37	0.14	0.85	1.00	0.00	0.00	0.37	0.52
+3.58	-1.00	0.16	0.68	-0.48	0.14	0.92	1.00	0.00	0.00	0.48	0.36
+3.60	-1.00	0.20	0.60	-0.59	0.14	0.78	1.00	0.00	0.00	0.59	0.20
+3.62	-1.00	0.24	0.52	-0.68	0.14	0.41	1.00	0.00	0.00	0.68	0.04
+3.64	-1.00	0.28	0.44	-0.77	0.43	0.90	1.00	0.00	0.00	0.77	-0.12
+3.66	-1.00	0.32	0.36	-0.84	0.43	0.71	1.00	0.00	0.00	0.84	-0.28
+3.68	-1.00	0.36	0.28	-0.90	0.43	0.94	1.00	0.00	0.00	0.90	-0.44
+3.70	-1.00	0.40	0.20	-0.95	0.43	0.92	1.00	0.00	0.00	0.95	-0.60
+3.72	-1.00	0.44	0.12	-0.98	0.43	0.91	1.00	0.00	0.00	0.98	-0.76
+3.74	-1.00	0.48	0.04	-1.00	0.43	0.79	1.00	0.00	0.00	1.00	-0.92
+3.76	-1.00	0.52	-0.04	-1.00	0.71	0.64	1.00	0.00	0.00	1.00	-1.00
+3.78	-1.00	0.56	-0.12	-0.98	0.71	0.08	1.00	0.00	0.00	0.98	-1.00
+3.80	-1.00	0.60	-0.20	-0.95	0.71	0.49	1.00	0.00	0.00	0.95	-1.00
+3.82	-1.00	0.64	-0.28	-0.90	0.71	0.50	1.00	0.00	0.00	0.90	-1.00
+3.84	-1.00	0.68	-0.36	-0.84	0.71	0.86	1.00	0.00	0.00	0.84	-1.00
+3.86	-1.00	0.72	-0.44	-0.77	0.71	0.61	1.00	0.00	0.00	0.77	-1.00
+3.88	-1.00	0.76	-0.52	-0.68	1.00	0.42	1.00	0.00	0.00	0.68	-1.00
+3.90	-1.00	0.80	-0.60	-0.59	1.00	0.25	1.00	0.00	0.00	0.59	-1.00
+3.92	-1.00	0.84	-0.68	-0.48	1.00	0.06	1.00	0.00	0.00	0.48	-1.00
+3.94	-1.00	0.88	-0.76	-0.37	1.00	0.97	1.00	0.00	0.00	0.37	-1.00
+3.96	-1.00	0.92	-0.84	-0.25	1.00	0.81	1.00	0.00	0.00	0.25	-1.00
+3.98	-1.00	0.96	-0.92	-0.13	1.00	0.57	1.00	0.00	0.00	0.13	-1.00
+
+done...

libraries/FunctionGenerator/examples/functionGeneratorPerformance/performance_0.3.0.txt

@@ -0,0 +1,429 @@
+
+functionGeneratorPerformance.ino
+FUNCTIONGENERATOR_LIB_VERSION: 0.3.0
+
+indicative output Arduino UNO 1.8.19, 16 MHz.
+
+| wave form name |  usec  |  max calls/sec  |
+|:---------------|-------:|----------------:|
+| square         |  54.57 |       18325.49  |
+| sawtooth       |  61.69 |       16210.61  |
+| triangle       |  79.80 |       12531.96  |
+| sinus          | 166.38 |        6010.37  |
+| stair          |  80.86 |       12366.38  |
+| random         |  42.61 |       23466.69  |
+| random_DC      |  67.18 |       14885.12  |
+| line           |   0.76 |     1322751.37  |
+| zero           |   0.75 |     1324854.25  |
+| sinusDiode     | 169.93 |        5884.79  |
+| sinusRectified | 169.49 |        5900.03  |
+| trapezium1     | 100.98 |        9903.30  |
+| trapezium2     | 143.98 |        6945.58  |
+| heartBeat      | 128.52 |        7780.77  |
+| freeWave       |  75.52 |       13241.31  |
+
+
+
+t 	 sqr	 saw	 tri	 sin	 str	 rnd	 line	 zero	 sinD	 sinR	 trap
+-4.00	-1.00	1.00	-1.00	-0.00	1.00	0.50	1.00	0.00	0.00	0.00	-1.00
+-3.98	1.00	-0.96	-0.92	0.13	-1.00	0.06	1.00	0.00	0.13	0.13	-1.00
+-3.96	1.00	-0.92	-0.84	0.25	-1.00	0.34	1.00	0.00	0.25	0.25	-1.00
+-3.94	1.00	-0.88	-0.76	0.37	-1.00	0.33	1.00	0.00	0.37	0.37	-1.00
+-3.92	1.00	-0.84	-0.68	0.48	-1.00	0.95	1.00	0.00	0.48	0.48	-1.00
+-3.90	1.00	-0.80	-0.60	0.59	-1.00	0.75	1.00	0.00	0.59	0.59	-1.00
+-3.88	1.00	-0.76	-0.52	0.68	-1.00	0.20	1.00	0.00	0.68	0.68	-1.00
+-3.86	1.00	-0.72	-0.44	0.77	-0.71	0.33	1.00	0.00	0.77	0.77	-1.00
+-3.84	1.00	-0.68	-0.36	0.84	-0.71	0.25	1.00	0.00	0.84	0.84	-1.00
+-3.82	1.00	-0.64	-0.28	0.90	-0.71	0.39	1.00	0.00	0.90	0.90	-1.00
+-3.80	1.00	-0.60	-0.20	0.95	-0.71	0.42	1.00	0.00	0.95	0.95	-1.00
+-3.78	1.00	-0.56	-0.12	0.98	-0.71	0.95	1.00	0.00	0.98	0.98	-1.00
+-3.76	1.00	-0.52	-0.04	1.00	-0.71	0.56	1.00	0.00	1.00	1.00	-1.00
+-3.74	1.00	-0.48	0.04	1.00	-0.43	0.64	1.00	0.00	1.00	1.00	-0.92
+-3.72	1.00	-0.44	0.12	0.98	-0.43	0.17	1.00	0.00	0.98	0.98	-0.76
+-3.70	1.00	-0.40	0.20	0.95	-0.43	0.78	1.00	0.00	0.95	0.95	-0.60
+-3.68	1.00	-0.36	0.28	0.90	-0.43	0.02	1.00	0.00	0.90	0.90	-0.44
+-3.66	1.00	-0.32	0.36	0.84	-0.43	0.31	1.00	0.00	0.84	0.84	-0.28
+-3.64	1.00	-0.28	0.44	0.77	-0.43	0.49	1.00	0.00	0.77	0.77	-0.12
+-3.62	1.00	-0.24	0.52	0.68	-0.14	0.09	1.00	0.00	0.68	0.68	0.04
+-3.60	1.00	-0.20	0.60	0.59	-0.14	0.21	1.00	0.00	0.59	0.59	0.20
+-3.58	1.00	-0.16	0.68	0.48	-0.14	0.82	1.00	0.00	0.48	0.48	0.36
+-3.56	1.00	-0.12	0.76	0.37	-0.14	0.51	1.00	0.00	0.37	0.37	0.52
+-3.54	1.00	-0.08	0.84	0.25	-0.14	0.74	1.00	0.00	0.25	0.25	0.68
+-3.52	1.00	-0.04	0.92	0.13	-0.14	0.20	1.00	0.00	0.13	0.13	0.84
+-3.50	1.00	0.00	1.00	0.00	-0.14	0.27	1.00	0.00	0.00	0.00	1.00
+-3.48	-1.00	0.04	0.92	-0.13	0.14	0.15	1.00	0.00	0.00	0.13	1.00
+-3.46	-1.00	0.08	0.84	-0.25	0.14	0.67	1.00	0.00	0.00	0.25	1.00
+-3.44	-1.00	0.12	0.76	-0.37	0.14	0.54	1.00	0.00	0.00	0.37	1.00
+-3.42	-1.00	0.16	0.68	-0.48	0.14	0.44	1.00	0.00	0.00	0.48	1.00
+-3.40	-1.00	0.20	0.60	-0.59	0.14	0.85	1.00	0.00	0.00	0.59	1.00
+-3.38	-1.00	0.24	0.52	-0.68	0.14	0.90	1.00	0.00	0.00	0.68	1.00
+-3.36	-1.00	0.28	0.44	-0.77	0.43	0.43	1.00	0.00	0.00	0.77	1.00
+-3.34	-1.00	0.32	0.36	-0.84	0.43	0.11	1.00	0.00	0.00	0.84	1.00
+-3.32	-1.00	0.36	0.28	-0.90	0.43	0.91	1.00	0.00	0.00	0.90	1.00
+-3.30	-1.00	0.40	0.20	-0.95	0.43	0.79	1.00	0.00	0.00	0.95	1.00
+-3.28	-1.00	0.44	0.12	-0.98	0.43	0.17	1.00	0.00	0.00	0.98	1.00
+-3.26	-1.00	0.48	0.04	-1.00	0.43	0.72	1.00	0.00	0.00	1.00	1.00
+-3.24	-1.00	0.52	-0.04	-1.00	0.71	0.77	1.00	0.00	0.00	1.00	0.92
+-3.22	-1.00	0.56	-0.12	-0.98	0.71	0.86	1.00	0.00	0.00	0.98	0.76
+-3.20	-1.00	0.60	-0.20	-0.95	0.71	0.50	1.00	0.00	0.00	0.95	0.60
+-3.18	-1.00	0.64	-0.28	-0.90	0.71	0.42	1.00	0.00	0.00	0.90	0.44
+-3.16	-1.00	0.68	-0.36	-0.84	0.71	0.73	1.00	0.00	0.00	0.84	0.28
+-3.14	-1.00	0.72	-0.44	-0.77	0.71	0.01	1.00	0.00	0.00	0.77	0.12
+-3.12	-1.00	0.76	-0.52	-0.68	1.00	0.52	1.00	0.00	0.00	0.68	-0.04
+-3.10	-1.00	0.80	-0.60	-0.59	1.00	0.72	1.00	0.00	0.00	0.59	-0.20
+-3.08	-1.00	0.84	-0.68	-0.48	1.00	0.61	1.00	0.00	0.00	0.48	-0.36
+-3.06	-1.00	0.88	-0.76	-0.37	1.00	0.41	1.00	0.00	0.00	0.37	-0.52
+-3.04	-1.00	0.92	-0.84	-0.25	1.00	0.68	1.00	0.00	0.00	0.25	-0.68
+-3.02	-1.00	0.96	-0.92	-0.13	1.00	0.34	1.00	0.00	0.00	0.13	-0.84
+-3.00	-1.00	1.00	-1.00	-0.00	1.00	0.90	1.00	0.00	0.00	0.00	-1.00
+-2.98	1.00	-0.96	-0.92	0.13	-1.00	0.43	1.00	0.00	0.13	0.13	-1.00
+-2.96	1.00	-0.92	-0.84	0.25	-1.00	0.47	1.00	0.00	0.25	0.25	-1.00
+-2.94	1.00	-0.88	-0.76	0.37	-1.00	0.51	1.00	0.00	0.37	0.37	-1.00
+-2.92	1.00	-0.84	-0.68	0.48	-1.00	0.29	1.00	0.00	0.48	0.48	-1.00
+-2.90	1.00	-0.80	-0.60	0.59	-1.00	0.42	1.00	0.00	0.59	0.59	-1.00
+-2.88	1.00	-0.76	-0.52	0.68	-1.00	0.02	1.00	0.00	0.68	0.68	-1.00
+-2.86	1.00	-0.72	-0.44	0.77	-0.71	0.91	1.00	0.00	0.77	0.77	-1.00
+-2.84	1.00	-0.68	-0.36	0.84	-0.71	0.00	1.00	0.00	0.84	0.84	-1.00
+-2.82	1.00	-0.64	-0.28	0.90	-0.71	0.22	1.00	0.00	0.90	0.90	-1.00
+-2.80	1.00	-0.60	-0.20	0.95	-0.71	0.55	1.00	0.00	0.95	0.95	-1.00
+-2.78	1.00	-0.56	-0.12	0.98	-0.71	0.96	1.00	0.00	0.98	0.98	-1.00
+-2.76	1.00	-0.52	-0.04	1.00	-0.71	0.30	1.00	0.00	1.00	1.00	-1.00
+-2.74	1.00	-0.48	0.04	1.00	-0.43	0.19	1.00	0.00	1.00	1.00	-0.92
+-2.72	1.00	-0.44	0.12	0.98	-0.43	0.62	1.00	0.00	0.98	0.98	-0.76
+-2.70	1.00	-0.40	0.20	0.95	-0.43	0.61	1.00	0.00	0.95	0.95	-0.60
+-2.68	1.00	-0.36	0.28	0.90	-0.43	0.28	1.00	0.00	0.90	0.90	-0.44
+-2.66	1.00	-0.32	0.36	0.84	-0.43	0.85	1.00	0.00	0.84	0.84	-0.28
+-2.64	1.00	-0.28	0.44	0.77	-0.43	0.22	1.00	0.00	0.77	0.77	-0.12
+-2.62	1.00	-0.24	0.52	0.68	-0.14	0.66	1.00	0.00	0.68	0.68	0.04
+-2.60	1.00	-0.20	0.60	0.59	-0.14	0.62	1.00	0.00	0.59	0.59	0.20
+-2.58	1.00	-0.16	0.68	0.48	-0.14	0.30	1.00	0.00	0.48	0.48	0.36
+-2.56	1.00	-0.12	0.76	0.37	-0.14	0.38	1.00	0.00	0.37	0.37	0.52
+-2.54	1.00	-0.08	0.84	0.25	-0.14	0.00	1.00	0.00	0.25	0.25	0.68
+-2.52	1.00	-0.04	0.92	0.13	-0.14	0.09	1.00	0.00	0.13	0.13	0.84
+-2.50	1.00	0.00	1.00	0.00	-0.14	0.56	1.00	0.00	0.00	0.00	1.00
+-2.48	-1.00	0.04	0.92	-0.13	0.14	0.67	1.00	0.00	0.00	0.13	1.00
+-2.46	-1.00	0.08	0.84	-0.25	0.14	0.66	1.00	0.00	0.00	0.25	1.00
+-2.44	-1.00	0.12	0.76	-0.37	0.14	0.15	1.00	0.00	0.00	0.37	1.00
+-2.42	-1.00	0.16	0.68	-0.48	0.14	0.71	1.00	0.00	0.00	0.48	1.00
+-2.40	-1.00	0.20	0.60	-0.59	0.14	0.75	1.00	0.00	0.00	0.59	1.00
+-2.38	-1.00	0.24	0.52	-0.68	0.14	0.13	1.00	0.00	0.00	0.68	1.00
+-2.36	-1.00	0.28	0.44	-0.77	0.43	0.99	1.00	0.00	0.00	0.77	1.00
+-2.34	-1.00	0.32	0.36	-0.84	0.43	0.01	1.00	0.00	0.00	0.84	1.00
+-2.32	-1.00	0.36	0.28	-0.90	0.43	0.92	1.00	0.00	0.00	0.90	1.00
+-2.30	-1.00	0.40	0.20	-0.95	0.43	0.92	1.00	0.00	0.00	0.95	1.00
+-2.28	-1.00	0.44	0.12	-0.98	0.43	0.38	1.00	0.00	0.00	0.98	1.00
+-2.26	-1.00	0.48	0.04	-1.00	0.43	0.87	1.00	0.00	0.00	1.00	1.00
+-2.24	-1.00	0.52	-0.04	-1.00	0.71	0.42	1.00	0.00	0.00	1.00	0.92
+-2.22	-1.00	0.56	-0.12	-0.98	0.71	0.88	1.00	0.00	0.00	0.98	0.76
+-2.20	-1.00	0.60	-0.20	-0.95	0.71	0.71	1.00	0.00	0.00	0.95	0.60
+-2.18	-1.00	0.64	-0.28	-0.90	0.71	0.97	1.00	0.00	0.00	0.90	0.44
+-2.16	-1.00	0.68	-0.36	-0.84	0.71	0.27	1.00	0.00	0.00	0.84	0.28
+-2.14	-1.00	0.72	-0.44	-0.77	0.71	0.94	1.00	0.00	0.00	0.77	0.12
+-2.12	-1.00	0.76	-0.52	-0.68	1.00	0.92	1.00	0.00	0.00	0.68	-0.04
+-2.10	-1.00	0.80	-0.60	-0.59	1.00	0.02	1.00	0.00	0.00	0.59	-0.20
+-2.08	-1.00	0.84	-0.68	-0.48	1.00	0.26	1.00	0.00	0.00	0.48	-0.36
+-2.06	-1.00	0.88	-0.76	-0.37	1.00	0.54	1.00	0.00	0.00	0.37	-0.52
+-2.04	-1.00	0.92	-0.84	-0.25	1.00	0.93	1.00	0.00	0.00	0.25	-0.68
+-2.02	-1.00	0.96	-0.92	-0.13	1.00	0.25	1.00	0.00	0.00	0.13	-0.84
+-2.00	-1.00	1.00	-1.00	-0.00	1.00	0.77	1.00	0.00	0.00	0.00	-1.00
+-1.98	1.00	-0.96	-0.92	0.13	-1.00	0.71	1.00	0.00	0.13	0.13	-1.00
+-1.96	1.00	-0.92	-0.84	0.25	-1.00	0.86	1.00	0.00	0.25	0.25	-1.00
+-1.94	1.00	-0.88	-0.76	0.37	-1.00	0.15	1.00	0.00	0.37	0.37	-1.00
+-1.92	1.00	-0.84	-0.68	0.48	-1.00	0.80	1.00	0.00	0.48	0.48	-1.00
+-1.90	1.00	-0.80	-0.60	0.59	-1.00	0.17	1.00	0.00	0.59	0.59	-1.00
+-1.88	1.00	-0.76	-0.52	0.68	-1.00	0.18	1.00	0.00	0.68	0.68	-1.00
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+1.22	1.00	-0.56	-0.12	0.98	-0.71	0.05	1.00	0.00	0.98	0.98	0.76
+1.24	1.00	-0.52	-0.04	1.00	-0.71	0.93	1.00	0.00	1.00	1.00	0.92
+1.26	1.00	-0.48	0.04	1.00	-0.43	0.97	1.00	0.00	1.00	1.00	1.00
+1.28	1.00	-0.44	0.12	0.98	-0.43	0.34	1.00	0.00	0.98	0.98	1.00
+1.30	1.00	-0.40	0.20	0.95	-0.43	0.57	1.00	0.00	0.95	0.95	1.00
+1.32	1.00	-0.36	0.28	0.90	-0.43	0.60	1.00	0.00	0.90	0.90	1.00
+1.34	1.00	-0.32	0.36	0.84	-0.43	0.91	1.00	0.00	0.84	0.84	1.00
+1.36	1.00	-0.28	0.44	0.77	-0.43	0.96	1.00	0.00	0.77	0.77	1.00
+1.38	1.00	-0.24	0.52	0.68	-0.14	0.25	1.00	0.00	0.68	0.68	1.00
+1.40	1.00	-0.20	0.60	0.59	-0.14	0.56	1.00	0.00	0.59	0.59	1.00
+1.42	1.00	-0.16	0.68	0.48	-0.14	0.06	1.00	0.00	0.48	0.48	1.00
+1.44	1.00	-0.12	0.76	0.37	-0.14	0.75	1.00	0.00	0.37	0.37	1.00
+1.46	1.00	-0.08	0.84	0.25	-0.14	0.14	1.00	0.00	0.25	0.25	1.00
+1.48	1.00	-0.04	0.92	0.13	-0.14	0.92	1.00	0.00	0.13	0.13	1.00
+1.50	-1.00	0.00	1.00	-0.00	0.14	0.35	1.00	0.00	0.00	0.00	1.00
+1.52	-1.00	0.04	0.92	-0.13	0.14	0.32	1.00	0.00	0.00	0.13	0.84
+1.54	-1.00	0.08	0.84	-0.25	0.14	0.50	1.00	0.00	0.00	0.25	0.68
+1.56	-1.00	0.12	0.76	-0.37	0.14	0.97	1.00	0.00	0.00	0.37	0.52
+1.58	-1.00	0.16	0.68	-0.48	0.14	0.28	1.00	0.00	0.00	0.48	0.36
+1.60	-1.00	0.20	0.60	-0.59	0.14	0.43	1.00	0.00	0.00	0.59	0.20
+1.62	-1.00	0.24	0.52	-0.68	0.14	0.42	1.00	0.00	0.00	0.68	0.04
+1.64	-1.00	0.28	0.44	-0.77	0.43	0.87	1.00	0.00	0.00	0.77	-0.12
+1.66	-1.00	0.32	0.36	-0.84	0.43	0.20	1.00	0.00	0.00	0.84	-0.28
+1.68	-1.00	0.36	0.28	-0.90	0.43	0.51	1.00	0.00	0.00	0.90	-0.44
+1.70	-1.00	0.40	0.20	-0.95	0.43	0.34	1.00	0.00	0.00	0.95	-0.60
+1.72	-1.00	0.44	0.12	-0.98	0.43	0.26	1.00	0.00	0.00	0.98	-0.76
+1.74	-1.00	0.48	0.04	-1.00	0.43	0.04	1.00	0.00	0.00	1.00	-0.92
+1.76	-1.00	0.52	-0.04	-1.00	0.71	0.04	1.00	0.00	0.00	1.00	-1.00
+1.78	-1.00	0.56	-0.12	-0.98	0.71	0.60	1.00	0.00	0.00	0.98	-1.00
+1.80	-1.00	0.60	-0.20	-0.95	0.71	0.82	1.00	0.00	0.00	0.95	-1.00
+1.82	-1.00	0.64	-0.28	-0.90	0.71	0.23	1.00	0.00	0.00	0.90	-1.00
+1.84	-1.00	0.68	-0.36	-0.84	0.71	0.93	1.00	0.00	0.00	0.84	-1.00
+1.86	-1.00	0.72	-0.44	-0.77	0.71	0.31	1.00	0.00	0.00	0.77	-1.00
+1.88	-1.00	0.76	-0.52	-0.68	1.00	0.50	1.00	0.00	0.00	0.68	-1.00
+1.90	-1.00	0.80	-0.60	-0.59	1.00	0.08	1.00	0.00	0.00	0.59	-1.00
+1.92	-1.00	0.84	-0.68	-0.48	1.00	0.47	1.00	0.00	0.00	0.48	-1.00
+1.94	-1.00	0.88	-0.76	-0.37	1.00	0.30	1.00	0.00	0.00	0.37	-1.00
+1.96	-1.00	0.92	-0.84	-0.25	1.00	0.63	1.00	0.00	0.00	0.25	-1.00
+1.98	-1.00	0.96	-0.92	-0.13	1.00	0.59	1.00	0.00	0.00	0.13	-1.00
+2.00	1.00	-1.00	-1.00	0.00	-1.00	0.36	1.00	0.00	0.00	0.00	-1.00
+2.02	1.00	-0.96	-0.92	0.13	-1.00	0.53	1.00	0.00	0.13	0.13	-0.84
+2.04	1.00	-0.92	-0.84	0.25	-1.00	0.87	1.00	0.00	0.25	0.25	-0.68
+2.06	1.00	-0.88	-0.76	0.37	-1.00	0.18	1.00	0.00	0.37	0.37	-0.52
+2.08	1.00	-0.84	-0.68	0.48	-1.00	0.24	1.00	0.00	0.48	0.48	-0.36
+2.10	1.00	-0.80	-0.60	0.59	-1.00	0.27	1.00	0.00	0.59	0.59	-0.20
+2.12	1.00	-0.76	-0.52	0.68	-1.00	0.31	1.00	0.00	0.68	0.68	-0.04
+2.14	1.00	-0.72	-0.44	0.77	-0.71	0.06	1.00	0.00	0.77	0.77	0.12
+2.16	1.00	-0.68	-0.36	0.84	-0.71	0.64	1.00	0.00	0.84	0.84	0.28
+2.18	1.00	-0.64	-0.28	0.90	-0.71	0.30	1.00	0.00	0.90	0.90	0.44
+2.20	1.00	-0.60	-0.20	0.95	-0.71	0.75	1.00	0.00	0.95	0.95	0.60
+2.22	1.00	-0.56	-0.12	0.98	-0.71	0.87	1.00	0.00	0.98	0.98	0.76
+2.24	1.00	-0.52	-0.04	1.00	-0.71	0.96	1.00	0.00	1.00	1.00	0.92
+2.26	1.00	-0.48	0.04	1.00	-0.43	0.48	1.00	0.00	1.00	1.00	1.00
+2.28	1.00	-0.44	0.12	0.98	-0.43	0.54	1.00	0.00	0.98	0.98	1.00
+2.30	1.00	-0.40	0.20	0.95	-0.43	0.20	1.00	0.00	0.95	0.95	1.00
+2.32	1.00	-0.36	0.28	0.90	-0.43	0.64	1.00	0.00	0.90	0.90	1.00
+2.34	1.00	-0.32	0.36	0.84	-0.43	0.72	1.00	0.00	0.84	0.84	1.00
+2.36	1.00	-0.28	0.44	0.77	-0.43	0.07	1.00	0.00	0.77	0.77	1.00
+2.38	1.00	-0.24	0.52	0.68	-0.14	0.38	1.00	0.00	0.68	0.68	1.00
+2.40	1.00	-0.20	0.60	0.59	-0.14	0.51	1.00	0.00	0.59	0.59	1.00
+2.42	1.00	-0.16	0.68	0.48	-0.14	0.47	1.00	0.00	0.48	0.48	1.00
+2.44	1.00	-0.12	0.76	0.37	-0.14	0.93	1.00	0.00	0.37	0.37	1.00
+2.46	1.00	-0.08	0.84	0.25	-0.14	0.13	1.00	0.00	0.25	0.25	1.00
+2.48	1.00	-0.04	0.92	0.13	-0.14	0.80	1.00	0.00	0.13	0.13	1.00
+2.50	-1.00	0.00	1.00	-0.00	0.14	0.10	1.00	0.00	0.00	0.00	1.00
+2.52	-1.00	0.04	0.92	-0.13	0.14	0.61	1.00	0.00	0.00	0.13	0.84
+2.54	-1.00	0.08	0.84	-0.25	0.14	0.26	1.00	0.00	0.00	0.25	0.68
+2.56	-1.00	0.12	0.76	-0.37	0.14	0.40	1.00	0.00	0.00	0.37	0.52
+2.58	-1.00	0.16	0.68	-0.48	0.14	0.90	1.00	0.00	0.00	0.48	0.36
+2.60	-1.00	0.20	0.60	-0.59	0.14	0.77	1.00	0.00	0.00	0.59	0.20
+2.62	-1.00	0.24	0.52	-0.68	0.14	0.20	1.00	0.00	0.00	0.68	0.04
+2.64	-1.00	0.28	0.44	-0.77	0.43	0.54	1.00	0.00	0.00	0.77	-0.12
+2.66	-1.00	0.32	0.36	-0.84	0.43	0.88	1.00	0.00	0.00	0.84	-0.28
+2.68	-1.00	0.36	0.28	-0.90	0.43	1.00	1.00	0.00	0.00	0.90	-0.44
+2.70	-1.00	0.40	0.20	-0.95	0.43	0.38	1.00	0.00	0.00	0.95	-0.60
+2.72	-1.00	0.44	0.12	-0.98	0.43	0.82	1.00	0.00	0.00	0.98	-0.76
+2.74	-1.00	0.48	0.04	-1.00	0.43	0.92	1.00	0.00	0.00	1.00	-0.92
+2.76	-1.00	0.52	-0.04	-1.00	0.71	0.88	1.00	0.00	0.00	1.00	-1.00
+2.78	-1.00	0.56	-0.12	-0.98	0.71	0.90	1.00	0.00	0.00	0.98	-1.00
+2.80	-1.00	0.60	-0.20	-0.95	0.71	0.48	1.00	0.00	0.00	0.95	-1.00
+2.82	-1.00	0.64	-0.28	-0.90	0.71	0.57	1.00	0.00	0.00	0.90	-1.00
+2.84	-1.00	0.68	-0.36	-0.84	0.71	0.60	1.00	0.00	0.00	0.84	-1.00
+2.86	-1.00	0.72	-0.44	-0.77	0.71	0.49	1.00	0.00	0.00	0.77	-1.00
+2.88	-1.00	0.76	-0.52	-0.68	1.00	0.60	1.00	0.00	0.00	0.68	-1.00
+2.90	-1.00	0.80	-0.60	-0.59	1.00	0.79	1.00	0.00	0.00	0.59	-1.00
+2.92	-1.00	0.84	-0.68	-0.48	1.00	0.35	1.00	0.00	0.00	0.48	-1.00
+2.94	-1.00	0.88	-0.76	-0.37	1.00	0.39	1.00	0.00	0.00	0.37	-1.00
+2.96	-1.00	0.92	-0.84	-0.25	1.00	0.85	1.00	0.00	0.00	0.25	-1.00
+2.98	-1.00	0.96	-0.92	-0.13	1.00	0.84	1.00	0.00	0.00	0.13	-1.00
+3.00	1.00	-1.00	-1.00	0.00	-1.00	0.30	1.00	0.00	0.00	0.00	-1.00
+3.02	1.00	-0.96	-0.92	0.13	-1.00	0.76	1.00	0.00	0.13	0.13	-0.84
+3.04	1.00	-0.92	-0.84	0.25	-1.00	0.07	1.00	0.00	0.25	0.25	-0.68
+3.06	1.00	-0.88	-0.76	0.37	-1.00	0.09	1.00	0.00	0.37	0.37	-0.52
+3.08	1.00	-0.84	-0.68	0.48	-1.00	0.22	1.00	0.00	0.48	0.48	-0.36
+3.10	1.00	-0.80	-0.60	0.59	-1.00	0.86	1.00	0.00	0.59	0.59	-0.20
+3.12	1.00	-0.76	-0.52	0.68	-1.00	0.04	1.00	0.00	0.68	0.68	-0.04
+3.14	1.00	-0.72	-0.44	0.77	-0.71	0.80	1.00	0.00	0.77	0.77	0.12
+3.16	1.00	-0.68	-0.36	0.84	-0.71	0.83	1.00	0.00	0.84	0.84	0.28
+3.18	1.00	-0.64	-0.28	0.90	-0.71	0.23	1.00	0.00	0.90	0.90	0.44
+3.20	1.00	-0.60	-0.20	0.95	-0.71	0.49	1.00	0.00	0.95	0.95	0.60
+3.22	1.00	-0.56	-0.12	0.98	-0.71	0.77	1.00	0.00	0.98	0.98	0.76
+3.24	1.00	-0.52	-0.04	1.00	-0.71	0.78	1.00	0.00	1.00	1.00	0.92
+3.26	1.00	-0.48	0.04	1.00	-0.43	0.35	1.00	0.00	1.00	1.00	1.00
+3.28	1.00	-0.44	0.12	0.98	-0.43	0.99	1.00	0.00	0.98	0.98	1.00
+3.30	1.00	-0.40	0.20	0.95	-0.43	0.14	1.00	0.00	0.95	0.95	1.00
+3.32	1.00	-0.36	0.28	0.90	-0.43	0.05	1.00	0.00	0.90	0.90	1.00
+3.34	1.00	-0.32	0.36	0.84	-0.43	0.70	1.00	0.00	0.84	0.84	1.00
+3.36	1.00	-0.28	0.44	0.77	-0.43	0.82	1.00	0.00	0.77	0.77	1.00
+3.38	1.00	-0.24	0.52	0.68	-0.14	0.62	1.00	0.00	0.68	0.68	1.00
+3.40	1.00	-0.20	0.60	0.59	-0.14	0.01	1.00	0.00	0.59	0.59	1.00
+3.42	1.00	-0.16	0.68	0.48	-0.14	0.69	1.00	0.00	0.48	0.48	1.00
+3.44	1.00	-0.12	0.76	0.37	-0.14	0.19	1.00	0.00	0.37	0.37	1.00
+3.46	1.00	-0.08	0.84	0.25	-0.14	0.39	1.00	0.00	0.25	0.25	1.00
+3.48	1.00	-0.04	0.92	0.13	-0.14	0.39	1.00	0.00	0.13	0.13	1.00
+3.50	-1.00	0.00	1.00	-0.00	0.14	0.46	1.00	0.00	0.00	0.00	1.00
+3.52	-1.00	0.04	0.92	-0.13	0.14	0.75	1.00	0.00	0.00	0.13	0.84
+3.54	-1.00	0.08	0.84	-0.25	0.14	0.21	1.00	0.00	0.00	0.25	0.68
+3.56	-1.00	0.12	0.76	-0.37	0.14	0.85	1.00	0.00	0.00	0.37	0.52
+3.58	-1.00	0.16	0.68	-0.48	0.14	0.92	1.00	0.00	0.00	0.48	0.36
+3.60	-1.00	0.20	0.60	-0.59	0.14	0.78	1.00	0.00	0.00	0.59	0.20
+3.62	-1.00	0.24	0.52	-0.68	0.14	0.41	1.00	0.00	0.00	0.68	0.04
+3.64	-1.00	0.28	0.44	-0.77	0.43	0.90	1.00	0.00	0.00	0.77	-0.12
+3.66	-1.00	0.32	0.36	-0.84	0.43	0.71	1.00	0.00	0.00	0.84	-0.28
+3.68	-1.00	0.36	0.28	-0.90	0.43	0.94	1.00	0.00	0.00	0.90	-0.44
+3.70	-1.00	0.40	0.20	-0.95	0.43	0.92	1.00	0.00	0.00	0.95	-0.60
+3.72	-1.00	0.44	0.12	-0.98	0.43	0.91	1.00	0.00	0.00	0.98	-0.76
+3.74	-1.00	0.48	0.04	-1.00	0.43	0.79	1.00	0.00	0.00	1.00	-0.92
+3.76	-1.00	0.52	-0.04	-1.00	0.71	0.64	1.00	0.00	0.00	1.00	-1.00
+3.78	-1.00	0.56	-0.12	-0.98	0.71	0.08	1.00	0.00	0.00	0.98	-1.00
+3.80	-1.00	0.60	-0.20	-0.95	0.71	0.49	1.00	0.00	0.00	0.95	-1.00
+3.82	-1.00	0.64	-0.28	-0.90	0.71	0.50	1.00	0.00	0.00	0.90	-1.00
+3.84	-1.00	0.68	-0.36	-0.84	0.71	0.86	1.00	0.00	0.00	0.84	-1.00
+3.86	-1.00	0.72	-0.44	-0.77	0.71	0.61	1.00	0.00	0.00	0.77	-1.00
+3.88	-1.00	0.76	-0.52	-0.68	1.00	0.42	1.00	0.00	0.00	0.68	-1.00
+3.90	-1.00	0.80	-0.60	-0.59	1.00	0.25	1.00	0.00	0.00	0.59	-1.00
+3.92	-1.00	0.84	-0.68	-0.48	1.00	0.06	1.00	0.00	0.00	0.48	-1.00
+3.94	-1.00	0.88	-0.76	-0.37	1.00	0.97	1.00	0.00	0.00	0.37	-1.00
+3.96	-1.00	0.92	-0.84	-0.25	1.00	0.81	1.00	0.00	0.00	0.25	-1.00
+3.98	-1.00	0.96	-0.92	-0.13	1.00	0.57	1.00	0.00	0.00	0.13	-1.00
+
+done...

libraries/FunctionGenerator/examples/functionGeneratorPlotter/functionGeneratorPlotter.ino

@@ -11,17 +11,26 @@
 #include "functionGenerator.h"
 
 funcgen gen;
+funcgen gen2;
 
 
 void setup()
 {
   Serial.begin(115200);
-  //  Serial.print("Start functionGeneratorPerformance - LIB VERSION: ");
+  //  Serial.println(__FILE__);
+  //  Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
   //  Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
+  //  Serial.println();
 
-  gen.setAmplitude(50);
+  gen.setAmplitude(80);
-  gen.setFrequency(1);
+  gen.setFrequency(65.0 / 60.0); //  HB = BPM/60.0
-  gen.setDutyCycle(25);
+  gen.setDutyCycle(40);
+  gen2.setYShift(+20);
+
+  gen2.setAmplitude(80);
+  gen2.setFrequency(120.0 / 60.0); //  HB = BPM/60.0
+  gen2.setDutyCycle(80);
+  gen2.setYShift(-80);
 }
 
 
@@ -34,20 +43,34 @@ void loop()
 
   //  Serial.print(t, 3);
   //  Serial.print("\t");
-  Serial.print(80);
+  Serial.print(100);
   Serial.print("\t");
-  Serial.print(-80);
+  Serial.print(-100);
-  Serial.print("\t");
-  Serial.print(gen.square(t));
   Serial.print("\t");
+  //  Serial.print(gen.square(t));
+  //  Serial.print("\t");
   //  Serial.print(gen.sawtooth(t, 0));  //  up    /|   signal
   //  Serial.print("\t");
   //  Serial.print(gen.sawtooth(t, 1));  //  down  |\   signal
   //  Serial.print("\t");
-  Serial.print(gen.triangle(t));
+  //  Serial.print(gen.triangle(t));
   //  Serial.print("\t");
   //  Serial.print(gen.sinus(t));
   //  Serial.print("\t");
+  //  Serial.print(gen.sinusDiode(t));
+  //  Serial.print("\t");
+  //  Serial.print(gen.sinusRectified(t));
+  //  Serial.print("\t");
+  //  Serial.print(gen.trapezium1(t));
+  //  Serial.print("\t");
+  //  Serial.print(gen.trapezium2(t));
+  //  Serial.print("\t");
+  Serial.print(gen.heartBeat(t));
+  Serial.print("\t");
+  Serial.print(gen2.heartBeat(t));
+  //  Serial.print("\t");
+  //  Serial.print(gen.freeWave(t, array));
+  //  Serial.print("\t");
   //    Serial.print(gen.stair(t, 16, 0));  //  step up
   //    Serial.print("\t");
   //    Serial.print(gen.stair(t, 16, 1));  //  step down

libraries/FunctionGenerator/examples/generateFreeWave/generateFreeWave.ino

@@ -0,0 +1,36 @@
+//
+//    FILE: generatorFreeWave.ino
+//  AUTHOR: Rob Tillaart
+// PURPOSE: demo function generators
+//     URL: https://github.com/RobTillaart/FunctionGenerator
+
+
+void setup()
+{
+  Serial.begin(115200);
+  Serial.println(__FILE__);
+  Serial.println();
+  Serial.println();
+
+  Serial.println("int16_t arr[101] =\n{");
+  for (int i = 0; i < 101; i++)
+  {
+    //  sin(t) + 0.25*sin(5t)
+    float f = sin(i * 0.01 * 2 * PI);
+    float g = sin(i * 0.05 * 2 * PI);
+    int16_t v = 8000 * (f + 0.25 * g);
+    Serial.print("");
+    Serial.print(v);
+    Serial.print(",");
+    if (i > 0 and i % 5 == 0) Serial.println();
+  }
+  Serial.println("};");
+}
+
+
+void loop()
+{
+}
+
+
+//  -- END OF FILE --

libraries/FunctionGenerator/functionGenerator.cpp

@@ -1,7 +1,7 @@
 //
 //    FILE: functionGenerator.cpp
 //  AUTHOR: Rob Tillaart
-// VERSION: 0.2.6
+// VERSION: 0.3.0
 // PURPOSE: wave form generating functions (use with care)
 //     URL: https://github.com/RobTillaart/FunctionGenerator
 
@@ -240,7 +240,199 @@ float funcgen::random_DC()
 }
 
 
+/////////////////////////////////////////////////////////////
+//
+//  EXPERIMENTAL 0.2.7
+//
+float funcgen::sinusDiode(float t)
+{
+  float rv = sinus(t);
+  if (rv < _yShift) return _yShift;
+  return rv;
 
+  // float rv;
+  // t += _phase;
+  // rv = sin(t * _freq0);
+  // if (rv < 0) return _yShift;
+  // rv *= amplitude;
+  // rv += _yShift;
+  // return rv;
+}
+
+
+float funcgen::sinusRectified(float t)
+{
+  // float rv = sinus(t);
+  // if (rv < _yShift) return _yShift - rv;
+  // return rv;
+
+  float rv;
+  t += _phase;
+  rv = _amplitude * sin(t * _freq0);
+  if (rv < 0) rv = -rv;
+  rv += _yShift;
+  return rv;
+}
+
+
+float funcgen::trapezium1(float t)
+{
+  t += _phase + _period * _dutyCycle / 4;  //  zero point for t = 0
+  if (t < 0)
+  {
+    t = -t;
+  }
+  t = fmod(t, _period);
+
+  if (t < _period * 0.5 * _dutyCycle)  //  rising part
+  {
+    return _yShift + -_amplitude + 2 * _amplitude * (t * 2  / (_period * _dutyCycle));
+  }
+  else if (t < _period * 0.5)  //  high part
+  {
+    return _yShift + _amplitude;
+  }
+  else if (t < _period * (0.5 + 0.5 * _dutyCycle))  //  falling part
+  {
+    return _yShift + _amplitude - 2 * _amplitude * ( (t * 2 - _period) / (_period * _dutyCycle));
+  }
+  else   //  low part
+  {
+    return _yShift + -_amplitude;
+  }
+}
+
+
+float funcgen::trapezium2(float t)
+{
+  t += _phase + _period * _dutyCycle / 4;  //  zero point for t = 0
+  if (t < 0)
+  {
+    t = -t;
+  }
+  t = fmod(t, _period);
+
+  if (t < _period * 0.25)  //  rising part
+  {
+    return _yShift + -_amplitude + 2 * _amplitude * (t * 4 / _period);
+  }
+  else if (t < _period * (0.25 + 0.5 * _dutyCycle))  //  high part
+  {
+    return _yShift + _amplitude;
+  }
+  else if (t < _period * (0.5 + 0.5 * _dutyCycle))  //  falling part
+  {
+    return _yShift + _amplitude - 2 * _amplitude * ((t - _period * (0.25 + 0.5 * _dutyCycle)) * 4 / _period);
+  }
+  else   //  low part
+  {
+    return _yShift + -_amplitude;
+  }
+}
+
+
+/*
+// no DC version (50%
+float funcgen::trapezium(float t)
+{
+  t += _phase;
+  if (t < 0)
+  {
+    t = -t;
+  }
+  t = fmod(t, _period);
+
+  if (t < _period * 0.25)  //  rising part
+  {
+    return -_amplitude + 2 * _amplitude * (t * 4 / _period);
+  }
+  else if (t < _period * 0.5)  //  high part
+  {
+    return _amplitude;
+  }
+  else if (t < _period * 0.75)  //  high part
+  {
+    return _amplitude - 2 * _amplitude * ((t - _period/2) * 4 / _period);
+  }
+  else   //  low part
+  {
+    return -_amplitude;
+  }
+}
+*/
+
+
+//
+//  EXPERIMENTAL HEARTBEAT  
+//  => setFrequency(72.0 / 60.0);  //  BPM/60 = BPS.
+float funcgen::heartBeat(float t)
+{
+  int16_t out[32] = {
+       0,    0, 1000, 2500,
+    1000, 1000,  -50, 10000,
+    -2500, 2000, 2500, 3000,
+    3000, 2000,    0,    0,
+    0,0,0,0,
+    0,0,0,0,
+    0,0,0,0,
+    0,0,0,0,
+  };
+  //  use duty cycle to determine zero level duration.
+  int pts = map(_dutyCycle * 100, 0, 100, 31, 15);
+  
+  return freeWave(t, out, pts);
+}
+
+
+/*
+//  points need to  be optimized, 
+//  0.2.7 uses 160 bytes for the two arrays.
+//  wrapper around freeWave?
+float funcgen::heartBeat(float t)
+{
+  //  based upon MultiMap in[] array is normalized to 0.0 - 1.0
+  //  Heart beat phase                 P                 Q     R     S                     T         U          
+  float in[21]  = { 0.0, 0.07, 0.13, 0.20, 0.27, 0.33,  0.40, 0.46,  0.53, 0.60, 0.66, 0.73, 0.80, 0.86, 0.93, 1.00 };
+  float out[21] = { 0.0, 0.00, 0.10, 0.25, 0.10, 0.10, -0.05, 1.00, -0.25, 0.20, 0.25, 0.30, 0.30, 0.20, 0.00, 0.00 };
+
+  t += _phase;
+  t = fmod(t, _period);
+
+  //  normalize t to 0.0 - 1.0
+  t *= _freq1;
+  //  search interval
+  int idx = 0; 
+  while (t > in[idx]) idx++;
+  if (t == in[idx]) return _yShift + _amplitude * out[idx];
+  idx--;
+  //  interpolate.
+  float factor = (t - in[idx]) / (in[idx+1] - in[idx]);
+  return _yShift + _amplitude * (out[idx] + factor * (out[idx+1] - out[idx]));
+}
+*/
+
+
+float funcgen::freeWave(float t, int16_t * arr, int16_t size)
+{
+  t += _phase;
+  //  normalize t to 0.0 - 1.0
+  t = fmod(t, _period);
+  t *= _freq1;
+
+  //  search interval, as arr is based upon N equidistant points,
+  //  we can easily calculate the points for direct access
+  float factor = t * size;
+  int idx = factor;        //  truncate to get index of output array.
+  factor = factor - idx;   //  remainder is interpolate factor.
+  //  interpolate.
+  return _yShift + _amplitude * 1e-4 * (arr[idx] + factor * (arr[idx+1] - arr[idx]));
+}
+
+
+/////////////////////////////////////////////////////////////
+//
+//  PRIVATE
+//
 //  An example of a simple pseudo-random number generator is the
 //  Multiply-with-carry method invented by George Marsaglia.
 //  two initializers (not null)
@@ -252,6 +444,7 @@ uint32_t funcgen::_random()
 }
 
 
+
 /////////////////////////////////////////////////////////////
 //
 //  INTEGER VERSIONS FOR 8 BIT DAC
@@ -356,6 +549,7 @@ float fgstr(float t, float period = 1.0, uint16_t steps = 8)
 //
 //  FULL floatS ONES
 //
+//  SAWTOOTH
 float fgsaw(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)
 {
   t += phase;
@@ -370,6 +564,7 @@ float fgsaw(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
 }
 
 
+//  TRIANGLE
 float fgtri(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, float dutyCycle = 0.50)
 {
   t += phase;
@@ -384,6 +579,7 @@ float fgtri(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
 }
 
 
+//  SQUARE
 float fgsqr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, float dutyCycle = 0.50)
 {
   t += phase;
@@ -400,6 +596,7 @@ float fgsqr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
 }
 
 
+//  SINUS
 float fgsin(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)
 {
   t += phase;
@@ -408,6 +605,7 @@ float fgsin(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
 }
 
 
+//  STAIR
 float fgstr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, uint16_t steps = 8)
 {
   t += phase;

libraries/FunctionGenerator/keywords.txt

@@ -27,8 +27,17 @@ zero	KEYWORD2
 sawtooth	KEYWORD2
 triangle	KEYWORD2
 square	KEYWORD2
+
 sinus	KEYWORD2
+sinusDiode	KEYWORD2
+sinusRectified	KEYWORD2
+
 stair	KEYWORD2
+trapezium1	KEYWORD2
+trapezium2	KEYWORD2
+
+heartBeat	KEYWORD2
+freeWave	KEYWORD2
 
 random	KEYWORD2
 random_DC	KEYWORD2

libraries/FunctionGenerator/library.json

@@ -15,7 +15,7 @@
     "type": "git",
     "url": "https://github.com/RobTillaart/FunctionGenerator"
   },
-  "version": "0.2.6",
+  "version": "0.3.0",
   "license": "MIT",
   "frameworks": "*",
   "platforms": "*",

libraries/FunctionGenerator/library.properties

@@ -1,5 +1,5 @@
 name=FunctionGenerator
-version=0.2.6
+version=0.3.0
 author=Rob Tillaart <rob.tillaart@gmail.com>
 maintainer=Rob Tillaart <rob.tillaart@gmail.com>
 sentence=Arduino library to generate wave forms (nummeric) for a DAC

libraries/FunctionGenerator/readme.md

@@ -27,10 +27,15 @@ In practice the generator is useful for low frequencies,
 Note: this class generates float values, performance wise this can be optimized,
 to achieve higher speeds at cost of accuracy / precision.
 
+As always, feedback and ideas are welcome.
 
-#### Performance
 
-Indication of what performance can be expected (based upon 0.2.1 version).  
+### Performance
+
+You always have to verify your own performance measurements to see if 
+your requirements are met by this library.
+
+**Indication** of what performance can be expected (based upon 0.2.1 version).  
 Note that the values need to be transported to a DAC or serial port too.  
 Numbers based on performance example, for one single signal.
 
@@ -72,14 +77,24 @@ have become slightly slower.
 |  Arduino UNO  |  16 MHz   |  square    |   57        |  1000 Hz   |
 |  Arduino UNO  |  16 MHz   |  random_DC |   68        |   500 Hz   |
 
+See **functionGeneratorPerformance.ino**
 
-#### Accuracy
+
+### Accuracy
 
 If the time parameter **t** grows large, the internal math may have rounding 
 problems after some time. This can and will affect the quality of the output.
+It is advised to reset **t** after a number (e.g. 100) full periods
 
 Needs further investigations.
 
+### Related
+
+- https://github.com/RobTillaart/AD9833 hardware waveform generator.
+- https://github.com/RobTillaart/AD985X hardware waveform generator.
+- https://github.com/RobTillaart/functionGenerator software waveform generator.
+- https://pages.mtu.edu/~suits/notefreqs.html frequency table for notes.
+
 
 ## Interface
 
@@ -87,40 +102,42 @@ Needs further investigations.
 #include "functionGenerator.h"
 ```
 
-#### Constructor
+### Constructor
 
 - **funcgen(float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)**
 All parameters (except duty cycle) can be set in the constructor but also later in configuration.
 Default dutyCycle is 50%.
 
 
-#### Configuration
+### Configuration
 
-- **void  setPeriod(float period = 1.0)** set the period of the wave in seconds. 
+- **void setPeriod(float period = 1.0)** set the period of the wave in seconds.
+This is the inverse of the frequency.
 - **float getPeriod()** returns the set period.
-- **void  setFrequency(float frequency = 1.0)** set the frequency of the wave in Hertz (1/s).
+- **void setFrequency(float frequency = 1.0)** set the frequency of the wave in Hertz (1/s).
+This is the inverse of the period.
 - **float getFrequency()** returns the set frequency in Hertz.
-- **void  setAmplitude(float amplitude = 1.0)** sets the amplitude of the wave.
+- **void setAmplitude(float amplitude = 1.0)** sets the amplitude of the wave.
 The range is from **-amplitude** to **+amplitude**.
 Setting the amplitude to 0 gives effectively a zero signal.
 Setting the amplitude to a negative value effectively inverts the signal.
 - **float getAmplitude()** returns the set amplitude.
-- **void  setPhase(float phase = 0.0)** shifts the phase of the wave. 
+- **void setPhase(float phase = 0.0)** shifts the phase of the wave. 
 Will only be noticeable when compared with other waves.
 Phase is also known as the X- or horizontal shift.
 - **float getPhase()** returns the set phase.
-- **void  setYShift(float yShift = 0.0)** sets an Y-shift or vertical offset in amplitude.
+- **void setYShift(float yShift = 0.0)** sets an Y-shift or vertical offset in amplitude.
 This allows to set e.g. the zero level.
 - **float getYShift()** returns the set Y-shift.
-- **void  setDutyCycle(float percentage = 100)** sets the duty cycle of the signal.
+- **void setDutyCycle(float percentage = 100)** sets the duty cycle of the signal.
 Experimental, not all waveforms have a duty cycle or interpret it differently, see below.
 Duty cycle must be between 0 and 100% and will be clipped otherwise.
-- **float getDutyCycle()** returns the set duty cycle.
+- **float getDutyCycle()** returns the set (clipped) duty cycle.
-- **void  setRandomSeed(uint32_t a, uint32_t b = 314159265)** sets the initial seeds for the
+- **void setRandomSeed(uint32_t a, uint32_t b = 314159265)** sets the initial seeds for the
 (Marsaglia) random number generator. The first is mandatory, the second is optional.
 
 
-#### Wave forms
+### Wave forms
 
 The variable t == time in seconds.
 
@@ -133,7 +150,8 @@ The variable t == time in seconds.
 - **float stair(float t, uint16_t steps = 8, uint8_t mode = 0)** defaults to 8 steps up.
   - mode = 0 ==> steps up
   - mode = 1 ==> steps down. Effectively equals inverting the amplitude.
-- **float random()** random noise generation.
+- **float random()** random noise generation between 0 and amplitude.
+Uses Marsaglia random generator.
 - **float line()** constant voltage line. 
 Height depends on the YShift and amplitude.
 - **float zero()** constant zero.
@@ -142,7 +160,29 @@ The functions **line()** and **zero()** can be used to drive a constant voltage
 from a DAC and can be used to calibrate the generator / DAC combination.
 
 
-#### Duty Cycle 
+Experimental 0.2.7
+
+- **float sinusDiode(float t)** sinus wave, only positive pulses.  
+(better name welcome).
+- **float sinusRectified(float t)** sinus wave, with "abs(negative pulses)".  
+(better name welcome).
+- **float trapezium1(float t)** trapezium wave.
+DutyCycle changes steepness of the falling and rising edge.
+The wave changes from a square wave, via trapezium to a triangle wave.
+- **float trapezium2(float t)** trapezium wave.
+DutyCycle changes duration HIGH vs LOW, wave stays trapezium like.
+Note at 50% DC the two trapezium functions are identical.
+- **float heartBeat(float t)** simplified heartbeat wave.
+To get a regular BPM heartbeat one should **setFrequency(BPM/60.0)** e.g 72/60 = 1.2.
+- **float freeWave(float t, int16_t arr, int16_t N)** define a free wave form.
+It uses an array of **N+1** values, dividing a full period in **N** equidistant steps.
+The last value should equal the first value to have a smooth transition.
+The values of the array normally vary between -10000 and +10000 to manage
+the set the relative amplitude in small steps. 
+These are scaled back to -1.0 to +1.0 times the amplitude.
+
+
+### Duty Cycle 
 
 Since 0.2.5 the library has **experimental** support for duty cycle.
 The meaning of duty cycle differs per wave form.
@@ -160,7 +200,16 @@ with respect to previous value.
 Implemented as a weighed average between new and previous value.
 Made a separate function as handling the duty cycle slows performance substantial.
 Initial starts at zero and can be adjusted with **YShift()**.
+- **float trapezium1(float t)** The duty cycle changes the steepness of the rising
+and falling edges. This changes the form from square wave to trapezium to triangle.
+The length of the HIGH LOW level go from 0 to half a period.
+- **float trapezium2(float t)** The duty cycle determines the length of the HIGH level,
+which is 0 for 0% DC and half a period for 100% DC. 
+The rising and falling edges stay same.
+- **float heartBeat(float t)** The duty cycle determines the part of the period
+that the signal ~zero.
 
+### No duty cycle
 
 The other functions need to be investigated what duty cycle means.
 Current ideas that are **NOT** implemented:
@@ -171,41 +220,52 @@ Think of it as the halve of the triangle wave.
 - **stair()** like sawtooth??
 - **line()** has no period so does not make sense (yet).
 - **zero()** has no period so does not make sense (yet).
-
+- **float sinusDiode(float t)**
-Feedback and ideas are welcome.
+- **float sinusRectified(float t)**
-
+- **float freeWave(float t, int16_t arr, int16_t N)**
 
 ## Future
 
-
 #### Must
 
-- documentation
+- improve documentation
-  - quality of signals - after substantial time t
+  - reorganize
-  - max freq per wave form etc.
+  - section per function might be better.
-    Should this be in the library?
-
 
 #### Should
 
 - smart reseed needed for random().
-- initialize random generator with compile time.
+  - initialize random generator with compile file + date + time.
-
+  - use function values for seed bits.
+- stand-alone functions in separate .h
+- clean up code
 
 #### Could
 
-- waves
+- ASDR wave 
-  - trapezium wave (could merge square and triangle and sawtooth)
+  - https://en.wikipedia.org/wiki/Envelope_(music)
-  - white noise, pink noise etc.
+  - **float ADSR(float t, float A, float D, float S, float R)** 
-- RC function curve.
+  - ADSR are percentages, A + D + R < 1.0
+  - S = % of amplitude.
 - external clock to synchronize two or more software function generators.
-- stand-alone functions in separate .h
 - check for synergy with https://github.com/RobTillaart/AD985X
 - investigate performance.
   - algorithms for DAC specific gains e.g. 10-12-16 bit.
   - improve performance sin() lookup table.
   - add float variable for ```_perDC = _period * _dutyCycle```
   - do we need **freq4** ? not since DC.
+- heartBeat
+  - small noise/variation parameter on amplitude and frequency.
+  - reduce footprint ==> wrapper around freeWave()
+- waves
+  - white noise, pink noise (better done with hardware)
+  - min() + max() => return +-amplitude + yshift?
+  - RC function curve.
+  - Gamma curve.
+- create a function table? with what?
+- create an example program to sample an arbitrary wave form
+  - output in the right format.
+  - slow sampling vs real time.
 
 
 #### Examples
@@ -228,6 +288,8 @@ Feedback and ideas are welcome.
   - **float stairDC()**
 - Bezier curve? (too complex)
 - record a signal and play back  ==> separate class
+- document max frequency per wave form etc.
+  Should this be in the library? differs per board.
 
 
 ## Support