from scipy.fftpack import fft
from numpy import sin,pi,cos,arange,linspace, where, reshape, size, angle
from pylab import plot,show, xlabel, title, figure, stem

fs=1000 #sampling frequency in Hz
f1=10   #frequency of first cosine
f2=20   #frequency of second cosine
f3=40   #frequency of third cosine
N=2000;
T=1.0*N/fs #analyzed time interval
t=arange(0,T,1.0/fs)

s=3*cos(2*pi*t*f1+5)+2*cos(2*pi*t*f2-2)+1*cos(2*pi*t*f3+3)

figure(1)
plot(t,s)
xlabel('Time [s]')
show()

S=fft(s)
figure(2)

f=arange(0,fs,fs/(1.0*N))  #discrete frequencies for FFT
magS=abs(S);
stem(f,magS);
show()

angleS=angle(S)
figure(3)
plot(f,angleS);
show()