PSet5 - FFT - Duplicate

import numpy as np import numpy.random as random from numpy.fft import fft import matplotlib.pyplot as plt %matplotlib inline

def sine_sampler(freq, sampling_rate, nsample, mean_noise, var_noise): t = np.arange(0, 1, 1/sampling_rate) xt = np.sin(freq*t) signal = xt + np.random.normal(scale=np.sqrt(var_noise), size=(nsample, )) return xt, signal, t fig, ax = plt.subplots(nrows=3, ncols=1, figsize = (24, 24)) sampling_rate = 300 tf = 1 n_sample = tf*sampling_rate mean_noise = 0 signal = np.zeros((3, n_sample)) for i, var_noise in enumerate([0, 0.1, 0.5]): xt_10, signal_10, t = sine_sampler(10, sampling_rate, n_sample, mean_noise, var_noise) xt_20, signal_20, _ = sine_sampler(20, sampling_rate, n_sample, mean_noise, var_noise) signal_ = signal_10 signal[i] = signal_ ax[i].plot(t, signal_) ax[i].set_title('Noise Variance: ' + str(var_noise) + ' Superimposed signal')

# Write code here sp = np.fft.fft(signal, axis = 1) fig, ax = plt.subplots(nrows=3, ncols=1, figsize = (24, 24)) ax[0].plot(sp[0]) ax[1].plot(sp[1]) ax[2].plot(sp[2])

# Write code here freq = np.fft.fftshift(np.fft.fftfreq(n_sample, d=1/sampling_rate)) sp = ft = np.fft.fftshift(np.fft.fft(signal, axis=1)) fig, ax = plt.subplots(nrows=3, ncols=1, figsize = (24, 24)) ax[0].scatter(freq, sp[0]) ax[1].scatter(freq, sp[1]) ax[2].scatter(freq, sp[2])

# Write answer here

# Do your filtering here and plot the frequency domain signals.

# Write your justification for your filtering here

# Do the IFFT and plot the signals in the time domain here.

# Write answer here

# Write answer/code here (ungraded)