WalshFUN

Walsh functions library for Arduino

The Walsh functions 1 are the discrete version of the sine-cosine functions. Walsh functions can be used analogus to sine-cosine functions in Fourier analysis or wave synthesis. According to the Walsh function definition, the output of the Walsh functions have only two states viz +1 or -1. With this implementation of the Walsh functions for Arduino, the walsh function output is a logic value of 1 or 0 (boolean).

The Walsh function is noted as:

WAL(n, t) , Where:

n is the 'frequency' or wave number,

t is the time, usually normalized to the time base t/T.

The even Walsh functions are sometimes labeled as CAL and the odd Walsh functions as SAL.

Walsh functions in the library

• bool wal8(unsigned char n, unsigned char t)
• bool wal16(unsigned char n, unsigned char t)
• bool wal32(unsigned char n, unsigned char t)
• bool wal64(unsigned char n, unsigned char t)
• bool wal128(unsigned char n, unsigned char t)
• bool wal256(unsigned char n, unsigned char t)

Examples

1. WalshFunctionSeries.ino - This example prints the first 32 Walsh functions in 32 timesteps. The logic '1' is printed as '+' and the logic '0' as '-'. See below.
2. WaveFormSynthesis1 - This example generates a sinewave from Walsh functions.
3. WaveFormSynthesis2 - This example generates a sawtooth wave from Walsh functions.

Tip: use the Arduino plotter function for example 2 and 3.

++++++++++++++++++++++++++++++++ WAL(0,T)
++++++++++++++++---------------- WAL(1,T)
++++++++----------------++++++++ WAL(2,T)
++++++++--------++++++++-------- WAL(3,T)
++++--------++++++++--------++++ WAL(4,T)
++++--------++++----++++++++---- WAL(5,T)
++++----++++--------++++----++++ WAL(6,T)
++++----++++----++++----++++---- WAL(7,T)
++----++++----++++----++++----++ WAL(8,T)
++----++++----++--++++----++++-- WAL(9,T)
++----++--++++----++++--++----++ WAL(10,T)
++----++--++++--++----++--++++-- WAL(11,T)
++--++----++--++++--++----++--++ WAL(12,T)
++--++----++--++--++--++++--++-- WAL(13,T)
++--++--++--++----++--++--++--++ WAL(14,T)
++--++--++--++--++--++--++--++-- WAL(15,T)
+--++--++--++--++--++--++--++--+ WAL(16,T)
+--++--++--++--+-++--++--++--++- WAL(17,T)
+--++--+-++--++--++--++-+--++--+ WAL(18,T)
+--++--+-++--++-+--++--+-++--++- WAL(19,T)
+--+-++--++-+--++--+-++--++-+--+ WAL(20,T)
+--+-++--++-+--+-++-+--++--+-++- WAL(21,T)
+--+-++-+--+-++--++-+--+-++-+--+ WAL(22,T)
+--+-++-+--+-++-+--+-++-+--+-++- WAL(23,T)
+-+--+-++-+--+-++-+--+-++-+--+-+ WAL(24,T)
+-+--+-++-+--+-+-+-++-+--+-++-+- WAL(25,T)
+-+--+-+-+-++-+--+-++-+-+-+--+-+ WAL(26,T)
+-+--+-+-+-++-+-+-+--+-+-+-++-+- WAL(27,T)
+-+-+-+--+-+-+-++-+-+-+--+-+-+-+ WAL(28,T)
+-+-+-+--+-+-+-+-+-+-+-++-+-+-+- WAL(29,T)
+-+-+-+-+-+-+-+--+-+-+-+-+-+-+-+ WAL(30,T)
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+- WAL(31,T)

++++++++++++++++---------------- SAL(1,T)
++++++++--------++++++++-------- SAL(2,T)
++++--------++++----++++++++---- SAL(3,T)
++++----++++----++++----++++---- SAL(4,T)
++----++++----++--++++----++++-- SAL(5,T)
++----++--++++--++----++--++++-- SAL(6,T)
++--++----++--++--++--++++--++-- SAL(7,T)
++--++--++--++--++--++--++--++-- SAL(8,T)
+--++--++--++--+-++--++--++--++- SAL(9,T)
+--++--+-++--++-+--++--+-++--++- SAL(10,T)
+--+-++--++-+--+-++-+--++--+-++- SAL(11,T)
+--+-++-+--+-++-+--+-++-+--+-++- SAL(12,T)
+-+--+-++-+--+-+-+-++-+--+-++-+- SAL(13,T)
+-+--+-+-+-++-+-+-+--+-+-+-++-+- SAL(14,T)
+-+-+-+--+-+-+-+-+-+-+-++-+-+-+- SAL(15,T)
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+- SAL(16,T)

++++++++----------------++++++++ CAL(1,T)
++++--------++++++++--------++++ CAL(2,T)
++++----++++--------++++----++++ CAL(3,T)
++----++++----++++----++++----++ CAL(4,T)
++----++--++++----++++--++----++ CAL(5,T)
++--++----++--++++--++----++--++ CAL(6,T)
++--++--++--++----++--++--++--++ CAL(7,T)
+--++--++--++--++--++--++--++--+ CAL(8,T)
+--++--+-++--++--++--++-+--++--+ CAL(9,T)
+--+-++--++-+--++--+-++--++-+--+ CAL(10,T)
+--+-++-+--+-++--++-+--+-++-+--+ CAL(11,T)
+-+--+-++-+--+-++-+--+-++-+--+-+ CAL(12,T)
+-+--+-+-+-++-+--+-++-+-+-+--+-+ CAL(13,T)
+-+-+-+--+-+-+-++-+-+-+--+-+-+-+ CAL(14,T)
+-+-+-+-+-+-+-+--+-+-+-+-+-+-+-+ CAL(15,T)