This notebook demonstrates the sampling and reconstruction of sinusoidal signals.
import numpy as np
import matplotlib.pyplot as plt
def sinusoid(samplingIndices, digitalFreq):
'''Compute a cosine'''
return np.cos(2*np.pi*digitalFreq*samplingIndices)
nData = 100
samplingFreq = 100 # Hz
samplingTime = 1/samplingFreq # s
samplingIndices = np.arange(nData)
time = samplingIndices*samplingTime
freqA = 10 # Hz
freqB = 90 # Hz (samplingFreq-freqA)
# plot the results
plt.figure(figsize=(10,6))
plt.plot(time, sinusoid(samplingIndices,freqA/samplingFreq), linewidth=2, marker='o', label="$x(t)$")
plt.plot(time, sinusoid(samplingIndices,freqB/samplingFreq), linewidth=2, marker='o', label="$y(t)$")
plt.legend()
plt.xlim((time[0],time[nData-1])), plt.ylim((-1.5,1.5))
plt.xlabel('time [s]'), plt.ylabel('Amplitude [.]');
plt.show()