In [19]: 
import scipy.signal

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))
In [12]: 
# sine100hzsamp.m : Simulated sampling of the 100Hz sine wave

f=100
time=0.05
Ts=1.0/10000.0
t = linspace(0, time, time/Ts)

w = sin(2*pi*f*t)

ss = 10

x = linspace(0, len(w)-1, len(w)/ss).astype(int)

wk = w.take(x)
ws = zeros(len(w))
ws.put(x,wk)

plot(t,w)
plot(t,ws,'r')
Out[12]:
[<matplotlib.lines.Line2D at 0x10cabf090>]

6.8. Modify sine100hzsamp.m to create an oversampled sinc wave, then sample this with ss=10. Repeate with 30,100,200. Comment on what's happening.

In [24]: 
f=100
time=0.05
Ts=1.0/10000.0
t = linspace(0, time, time/Ts)

w = sinc(2*pi*f*t)

plotspec(w, Ts)

for ss in [10,30,100,200]:
    x = linspace(0, len(w)-1, len(w)/ss).astype(int)

    wk = w.take(x)
    ws = zeros(len(w))
    ws.put(x,wk)

    plotspec(ws, Ts)

6.9. Plot hte spectrum of the 100Hz sine wave when it's downsampled by 10,11,30, and 200.

In [25]: 
f=100
time=0.05
Ts=1.0/10000.0
t = linspace(Ts, time, time/Ts)

w = sin(2*pi*f*t)

plotspec(w, Ts)

for ss in [10,11,30,200]:

    x = linspace(0, len(w)-1, len(w)/ss).astype(int)

    wk = w.take(x)
    ws = zeros(len(w))
    ws.put(x,wk)

    plotspec(ws, Ts)