def plotspec(x, Ts):
    fig = figure()
    ax1 = fig.add_subplot(211)
    ax1.plot(x)
    
    q = fft.fft(x)
    ax2 = fig.add_subplot(212)
    ax2.plot(fft.fftfreq(len(x), Ts), abs(q))
    
def arbspec(s, time, Ts):
    t = linspace(0.0, time, time/Ts)
    x = s(t)
    plotspec(x, Ts)
    
def speccos(f, phi, time, Ts):
    def s(t):
        return cos(2*pi*f*t+phi)
    arbspec(s, time, Ts)

3.11. With a sample rate of 100Hz, plot the spectrum of cosine waves with f=30,40,49,50,51,60Hz. Which show aliasing?

for f in [30,40,49,50,51,60]:
    speccos(f, 0, 2.0, 1.0/100.0)

3.12. Creating a cosine wave with f=50Hz, plot the spectrum with sampling rates of 50,90,100,110,200 Hz. Which show aliasing?

for Fs in [50,90,100,110,200]:
    speccos(50.0, 0, 2.0, 1.0/float(Fs))

3.13. Mimic the code in speccos.m with sampling interval Ts=1/100 to find the spectrum of square waves with fundamental f=10,20,30,33,43 Hz. Can you predict where the spikes will occu

def specsquare(f, time, Ts):
    t = linspace(0.0, time, time/Ts) # Create a time vector
    x = sign(cos(2*pi*f*t)) # Square wave = sign of cos wave
    plotspec(x, Ts)

Ts = 1.0/100.0

for f in [10,20,30,33,43]:
    specsquare(f, 2.0, Ts)