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}, "metadata": {} } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.signal import lfilter\n", "\n", "# Downsampling filter coefficients\n", "B = np.array([ 3.59810719e-04, 4.85152485e-04, -1.22140300e-18, -5.51059377e-04,\n", " -4.61749329e-04, 2.77255040e-04, 8.11721566e-04, 3.50339606e-04,\n", " -7.33001510e-04, -1.08649073e-03, 7.19282356e-18, 1.39801993e-03,\n", " 1.21125089e-03, -7.40454911e-04, -2.18014465e-03, -9.37542307e-04,\n", " 1.94138833e-03, 2.83487852e-03, -5.02629891e-18, -3.51319015e-03,\n", " -2.98232250e-03, 1.78613837e-03, 5.15442198e-03, 2.17422423e-03,\n", " -4.42079677e-03, -6.34655736e-03, 8.30873056e-18, 7.63494539e-03,\n", " 6.40090395e-03, -3.79254733e-03, -1.08471991e-02, -4.54368239e-03,\n", " 9.19339468e-03, 1.31633457e-02, -1.14868009e-17, -1.58738607e-02,\n", " -1.33839152e-02, 8.00343654e-03, 2.31983706e-02, 9.89613027e-03,\n", " -2.05125351e-02, -3.03090831e-02, 1.37742979e-17, 4.01369570e-02,\n", " 3.62695646e-02, -2.37930060e-02, -7.83586625e-02, -4.02378207e-02,\n", " 1.12033000e-01, 2.93555396e-01, 3.74671150e-01, 2.93555396e-01,\n", " 1.12033000e-01, -4.02378207e-02, -7.83586625e-02, -2.37930060e-02,\n", " 3.62695646e-02, 4.01369570e-02, 1.37742979e-17, -3.03090831e-02,\n", " -2.05125351e-02, 9.89613027e-03, 2.31983706e-02, 8.00343654e-03,\n", " -1.33839152e-02, -1.58738607e-02, -1.14868009e-17, 1.31633457e-02,\n", " 9.19339468e-03, -4.54368239e-03, -1.08471991e-02, -3.79254733e-03,\n", " 6.40090395e-03, 7.63494539e-03, 8.30873056e-18, -6.34655736e-03,\n", " -4.42079677e-03, 2.17422423e-03, 5.15442198e-03, 1.78613837e-03,\n", " -2.98232250e-03, -3.51319015e-03, -5.02629891e-18, 2.83487852e-03,\n", " 1.94138833e-03, -9.37542307e-04, -2.18014465e-03, -7.40454911e-04,\n", " 1.21125089e-03, 1.39801993e-03, 7.19282356e-18, -1.08649073e-03,\n", " -7.33001510e-04, 3.50339606e-04, 8.11721566e-04, 2.77255040e-04,\n", " -4.61749329e-04, -5.51059377e-04, -1.22140300e-18, 4.85152485e-04,\n", " 3.59810719e-04])\n", "\n", "#B = np.array([0.00074961181416, 0.00247663033476, 0.00146938649416, -0.00440446121505,\n", "# -0.00910635730662, 0.00000000000000, 0.02035676831506, 0.02233710562885,\n", "# -0.01712963672810, -0.06376620649567, -0.03590670035210, 0.10660980550088,\n", "# -0.29014909103794, 0.37500000000000, 0.29014909103794, 0.10660980550088,\n", "# -0.03590670035210, -0.06376620649567, -0.01712963672810, 0.02233710562885,\n", "# -0.02035676831506, 0.00000000000000, -0.00910635730662, -0.00440446121505,\n", "# -0.00146938649416, 0.00247663033476, 0.00074961181416])\n", "\n", "# Generate the 2048 samples\n", "fs = 8000 # Sampling rate\n", "N = 4096 # Number of samples\n", "M = 2 # Downsample factor\n", "n = np.arange(N)\n", "x = 5 * np.sin(n * np.pi / 4) + np.cos(5 * n * np.pi / 8)\n", "\n", "# Compute the single-sided amplitude spectrum\n", "X = 2 * np.abs(np.fft.fft(x, N)) / N\n", "X[0] = X[0] / 2\n", "\n", "# Map the frequency index up to the folding frequency in Hz\n", "f = np.arange(N // 2) * fs / N\n", "\n", "# Downsampling\n", "y = x[::M]\n", "NM = len(y)\n", "\n", "# Compute the single-sided amplitude spectrum for the downsampled signal\n", "Y = 2 * np.abs(np.fft.fft(y, NM)) / NM\n", "Y[0] = Y[0] / 2\n", "\n", "# Map the frequency index to the frequency in Hz for the downsampled signal\n", "fsM = np.arange(NM // 2) * (fs / M) / NM\n", "\n", "# Plot the amplitude spectra of the original and downsampled signals\n", "plt.figure(figsize=(12, 8))\n", "\n", "plt.subplot(2, 1, 1)\n", "plt.plot(f, X[:N // 2])\n", "plt.grid()\n", "plt.xlabel('Frequency (Hz)')\n", "plt.title('Amplitude Spectrum of Original Signal')\n", "\n", "plt.subplot(2, 1, 2)\n", "plt.plot(fsM, Y[:NM // 2])\n", "plt.grid()\n", "plt.xlabel('Frequency (Hz)')\n", "plt.title('Amplitude Spectrum of Downsampled Signal')\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "# Anti-aliasing filtering\n", "w = lfilter(B, 1, x)\n", "\n", "# Compute the single-sided amplitude spectrum for the filtered signal\n", "W = 2 * np.abs(np.fft.fft(w, N)) / N\n", "W[0] = W[0] / 2\n", "\n", "# Downsampling the filtered signal\n", "y_filtered = w[::M]\n", "NM_filtered = len(y_filtered)\n", "\n", "# Compute the single-sided amplitude spectrum for the downsampled filtered signal\n", "Y_filtered = 2 * np.abs(np.fft.fft(y_filtered, NM_filtered)) / NM_filtered\n", "Y_filtered[0] = Y_filtered[0] / 2\n", "\n", "# Plot the amplitude spectra of the filtered and downsampled filtered signals\n", "plt.figure(figsize=(12, 8))\n", "\n", "plt.subplot(2, 1, 1)\n", "plt.plot(f, W[:N // 2])\n", "plt.grid()\n", "plt.xlabel('Frequency (Hz)')\n", "plt.title('Amplitude Spectrum of Filtered Signal')\n", "\n", "plt.subplot(2, 1, 2)\n", "plt.plot(fsM, Y_filtered[:NM_filtered // 2])\n", "plt.grid()\n", "plt.xlabel('Frequency (Hz)')\n", "plt.title('Amplitude Spectrum of Downsampled Filtered Signal')\n", "\n", "plt.tight_layout()\n", "plt.show()\n" ] } ] }