"""
Illustrate correspondence between DCT bins and cosine signals.
"""
from scipy.fftpack import idct
from numpy import cos, arange, zeros, pi
import matplotlib.pyplot as plt
from numpy.testing import assert_allclose

N = 8  # only even numbers
k = arange(N)


###################################### Type 1
plt.figure(1)

sig = cos(2*pi*k/N)
plt.plot(k,   sig, '.-')
plt.plot(k+N, sig, '.-')

spectrum = zeros(N//2+1)
spectrum[1] = 1

plt.plot(k[:N//2+1], idct(spectrum, 1)/2, 'o-')
plt.margins(0, 0.1)

assert_allclose(sig[:N//2+1], idct(spectrum, 1)/2, rtol=1e-05, atol=1e-08)


###################################### Type 2
plt.figure(2)

sig = cos(2*pi*(k/N + 0.5/N))  # half-sample shift left
plt.plot(k,   sig, '.-')
plt.plot(k+N, sig, '.-')

spectrum = zeros(N//2)
spectrum[1] = 1

plt.plot(k[:N//2], idct(spectrum, 2)/2, 'o-')
plt.margins(0, 0.1)

assert_allclose(sig[:N//2], idct(spectrum, 2)/2, rtol=1e-05, atol=1e-08)

plt.show()