#Importing the fft and inverse fft functions from fftpackage
from scipy.fftpack import fft

#create an array with random n numbers
x = np.array([1.0, 2.0, 1.0, -1.0, 1.5])

#Applying the fft function
y = fft(x)
print y

[ 4.50000000+0.j           2.08155948-1.65109876j   -1.83155948+1.60822041j
 -1.83155948-1.60822041j   2.08155948+1.65109876j ]

#FFT is already in the workspace, using the same workspace to for inverse transform

yinv = ifft(y)

print yinv

[ 1.0+0.j   2.0+0.j   1.0+0.j   -1.0+0.j   1.5+0.j ]

import numpy as np
time_step = 0.02
period = 5.
time_vec = np.arange(0, 20, time_step)
sig = np.sin(2 * np.pi / period * time_vec) + 0.5 *np.random.randn(time_vec.size)
print sig.size

1000

from scipy import fftpack
sample_freq = fftpack.fftfreq(sig.size, d = time_step)
sig_fft = fftpack.fft(sig)
print sig_fft

array([ 
   25.45122234 +0.00000000e+00j,   6.29800973 +2.20269471e+00j,
   11.52137858 -2.00515732e+01j,   1.08111300 +1.35488579e+01j,
   …….])

from scipy.fftpack import dct
print dct(np.array([4., 3., 5., 10., 5., 3.]))

array([ 60.,  -3.48476592,  -13.85640646,  11.3137085,  6.,  -6.31319305])

from scipy.fftpack import dct
print idct(np.array([4., 3., 5., 10., 5., 3.]))

array([ 39.15085889, -20.14213562, -6.45392043, 7.13341236,
8.14213562, -3.83035081])