## show how fourier analysis allows you to reconstruct a square wave

## run this in the following manner:
# $ python four-sq.py > four-sq.out
# $ gnuplot
# plot [] [-1.2:1.2] 'four-sq.out' using 2 with lines
# replot 'four-sq.out' using 3 with lines
# replot 'four-sq.out' using 4 with lines
# replot 'four-sq.out' using 5 with lines
# replot 'four-sq.out' using 6 with lines
# replot 'four-sq.out' using 7 with lines
# replot 'four-sq.out' using 8 with lines
# pause -1
## or just do:
# $ python four-sq.py > four-sq.out
# $ gnuplot four-sq.gp

import math

def __main__():
  for i in range(100):
    t = i*2*math.pi/100.0
    print t, '    ', sq(t), ' ',
    for j in range(5):
      print '   ', sq_four(t, 2*j+1),
    print


## square wave from 0 to 2*PI
def sq(t):
  if t <= math.pi:
    return 1
  else:
    return -1

## square wave reconstructed with fourier series
def sq_four(t, n):
  val = 0
  for k in range(n+1):
    if k % 2 == 1:
      val += (4.0/(math.pi*k)) * math.sin(t*k)
  return val

__main__()