segment = sine_wave[0:51]
windowed_segment = segment * window

VI. Convolution & Correlation

• Perform linear convolution.

sig1 = np.repeat([0., 1., 0.], 100)
sig2 = np.repeat([0., 1., 1., 0.], 100)
convolved = signal.convolve(sig1, sig2, mode='same')

• Compute cross-correlation.

# Useful for finding delays between signals
correlation = signal.correlate(sig1, sig2, mode='full')

• Compute auto-correlation.

# Useful for finding periodicities in a signal
autocorr = signal.correlate(sine_wave, sine_wave, mode='full')

VII. Time-Frequency Analysis

• Compute and plot a spectrogram.

f, t_spec, Sxx = signal.spectrogram(chirp_signal, fs)
plt.pcolormesh(t_spec, f, Sxx, shading='gouraud')
plt.show()

• Perform Continuous Wavelet Transform (CWT).

widths = np.arange(1, 31)
cwt_matrix = signal.cwt(chirp_signal, signal.ricker, widths)

• Perform Hilbert transform to get the analytic signal.

analytic_signal = signal.hilbert(sine_wave)

• Calculate instantaneous frequency.

instant_phase = np.unwrap(np.angle(analytic_signal))
instant_freq = (np.diff(instant_phase) / (2.0*np.pi) * fs)

VIII. Feature Extraction

• Find peaks in a signal.

peaks, _ = signal.find_peaks(sine_wave, height=0.5)

• Find peaks with prominence criteria.

peaks_prom, _ = signal.find_peaks(noisy_signal, prominence=1)

• Differentiate a signal (e.g., to find velocity from position).

derivative = np.diff(sine_wave)

• Integrate a signal.

from scipy.integrate import cumulative_trapezoid
integral = cumulative_trapezoid(sine_wave, t, initial=0)

• Detrend a signal to remove a linear trend.

trend = np.linspace(0, 1, fs)
trended_signal = sine_wave + trend
detrended = signal.detrend(trended_signal)

IX. System Analysis

• Define a system via a transfer function (numerator, denominator).

# Example: 2nd order low-pass filter
system = signal.TransferFunction([1], [1, 1, 1])

• Compute the step response of a system.

t_step, y_step = signal.step(system)

• Compute the impulse response of a system.

t_impulse, y_impulse = signal.impulse(system)

• Compute the Bode plot of a system's frequency response.

w, mag, phase = signal.bode(system)

X. Signal Generation from Data

• Generate a signal from a function.

t = np.linspace(0, 1, 500)
custom_signal = np.sinc(2 * np.pi * 4 * t)

• Convert a list of values to a signal array.

my_data = [0, 1, 2, 3, 2, 1, 0, -1, -2, -1, 0]
data_signal = np.array(my_data)

• Read signal data from a WAV file.

from scipy.io import wavfile
samplerate, data = wavfile.read('audio.wav')

• Create a pulse train signal.

pulse_train = np.zeros(fs)
pulse_train[::100] = 1 # Impulse every 100 samples

#Python #SignalProcessing #SciPy #NumPy #DSP

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By: @DataScienceM ✨