#to start with marplotlib
#ipython --pylab

import numpy as np
from scipy.signal import tiang
from scipy.fftpack import fft

x = triang(15) #triangular function
x = fft(x)
mX = abs(X)
pX = np.angle(X)

#########################################

plot(x)
plot(mX) #magnitude and phase. first half are positive, second half are negative
plot(pX) #phase should be zero, why?  Because time signal was not centered around zero (it had a shift)

#########################################

#center around zero
x = triang(15)
fftbuffer = np.zeros(15)
fftbuffer[:8] = x[7:]  #from beginning to 8
fftbuffer[8:] = x[:7]  #from 8 to end
X = fft(fftbuffer)
mX = abs(X)
pX = np.angle(X)

#########################################

plot(fftbuffer) #v shaped
plot(mX) #magnitude spectrum.  no change
plot(pX) #phase is different