from numpy import array, arange, abs as np_abs
from numpy.fft import rfft, rfftfreq, fftshift
from numpy.random import uniform
from math import sin, cos, pi
import pylab
from random import gauss


def show_spectrum(sig, FD, N):
    spectrum = rfft(sig)
    pylab.plot(rfftfreq(N, 1./FD), np_abs(spectrum)/N)
    pylab.ylabel('voltage, mV')
    pylab.xlabel('frequency, Hz')
    pylab.grid(True)
    pylab.show()

FD = 22050
N = 2**10
F = 440.0
noise_g = [gauss(0.5, 0.05) for _ in range(N)]

sig1 = array([0.125*sin(2.*pi*F*n/FD + 2) for n in range(N)])
sig2 = array([sin(7.*pi*F*n/FD) for n in range(N)])
sig3 = array([6.*sin(2.*pi*F*n/FD + 2) for n in range(N)])
sig = sig3 + noise_g

show_spectrum(sig, FD, N)