75 lines
1.8 KiB
Python
75 lines
1.8 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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def DFT(x):
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"""
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Compute the Discrete Fourier Transform (DFT) of the input signal x.
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Parameters:
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x (array-like): Input signal
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Returns:
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X (array-like): DFT of the input signal
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"""
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N = len(x)
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n = np.arange(N)
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k = n.reshape((N, 1))
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e = np.exp(-2j * np.pi * k * n / N)
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X = np.dot(e, x)
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return X
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def DFTI(X):
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"""
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Compute the Inverse Discrete Fourier Transform (IDFT) of the input signal X.
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Parameters:
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X (array-like): Input signal
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Returns:
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x (array-like): IDFT of the input signal
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"""
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N = len(X)
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n = np.arange(N)
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k = n.reshape((N, 1))
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e = np.exp(2j * np.pi * k * n / N)
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x = np.dot(e, X) / N
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return x
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# Define a sine function as the input signal
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t = np.linspace(0, 1, 1000) # Time array
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frequency = 5 # Frequency of the sine wave
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x = np.sin(2 * np.pi * frequency * t) + np.sin(np.pi * frequency * t)
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# Compute the DFT of the sine wave
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X = DFT(x)
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# Plot the input signal
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plt.figure(figsize=(12, 4))
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plt.subplot(1, 3, 1)
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plt.plot(t, x)
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plt.title('Input Signal')
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plt.xlabel('Time')
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plt.ylabel('Amplitude')
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# Plot the magnitude spectrum (DFT)
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freq = np.fft.fftfreq(len(x), d=t[1]-t[0])
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plt.subplot(1, 3, 2)
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plt.stem(freq, np.abs(X))
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plt.title('Magnitude Spectrum (DFT)')
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plt.xlabel('Frequency')
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plt.ylabel('Magnitude')
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plt.xlim(-10, 10) # Limit the x-axis for better visualization
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# Compute the IDFT of the DFT signal
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x_reconstructed = DFTI(X)
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# Plot the reconstructed signal
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plt.subplot(1, 3, 3)
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plt.plot(t, x_reconstructed.real, label='Reconstructed Signal')
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plt.plot(t, x, label='Original Signal')
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plt.title('Reconstructed Signal vs Original Signal')
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plt.xlabel('Time')
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plt.ylabel('Amplitude')
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plt.legend()
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plt.tight_layout()
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plt.show()
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