from scipy import signal

slow_freq = 1e-4; fast_freq = 1e-2; num_samples = 1e5; t = np.arange(num_samples)

s = np.sin(2*np.pi*slow_freq*t) + .1 * np.sin(2*np.pi*fast_freq*t)

plot(s)

p,f=mlab.psd(s,NFFT=len(s), Fs=1)

plot(s[:10000])

loglog(f, p)

filter_hz = 1e-3

sampling_frequency = 1

b, a = signal.butter(5, filter_hz / (sampling_frequency/2.), btype='high')

print b,a

sf = signal.lfilter(b, a, s)

plot(sf)

plot(sf[:10000])

pf,ff=mlab.psd(sf,NFFT=len(s), Fs=1)

loglog(f, p, label="original"); loglog(ff, pf, label="filtered"); legend()