# NE MODIFIEZ PAS CE FICHIER import os import matplotlib.pyplot as plt import numpy as np def plot_1_1(t, x): plt.figure(figsize=(8, 4)) plt.plot(t, x, "*-") plt.title(r'Sampled signal $x(t)$') plt.xlabel('Time (s)') plt.ylabel(r'$x(t)$') # plt.grid() plt.show() def plot_1_2(f, real_X, imag_X, abs_X): _, axes = plt.subplots(nrows=1, ncols=3, figsize=(15, 4), sharex=True, sharey=True) # Real and imag parts axes[0].stem(f, real_X) axes[0].set_title("X(f), Real part") axes[1].stem(f, imag_X) axes[1].set_title("X(f), Imaginary part") # Absolute part axes[2].stem(f, abs_X, label="|X|") axes[2].set_title("X(f), Absolute value") # Shared legends _ = [a.set_xlabel("Frequency [Hz]") for a in axes] def plot_1_3(t, x1, x2, x, f, X): fig = plt.figure(figsize=(15, 6)) gs = fig.add_gridspec(3, 2) ax1 = fig.add_subplot(gs[0, 0]) ax2 = fig.add_subplot(gs[1, 0]) ax3 = fig.add_subplot(gs[2, 0]) ax4 = fig.add_subplot(gs[:, 1]) axes = [ax1, ax2, ax3, ax4] # Time domain axes[0].plot(t, x1) axes[0].set_title("$x_1(t)$") axes[1].plot(t, x2) axes[1].set_title("$x_2(t)$") axes[2].plot(t, x) axes[2].set_title("$x(t) = x_1(t) + x_2(t)$") _ = [a.set_xlabel("Time [s]") for a in axes[:3]] # Frequency axes[3].stem(f, np.abs(X)) axes[3].set_title("|X(f)|") axes[3].set_xlabel("Frequency [Hz]") # Fit all text in frame plt.tight_layout() def plot_1_4(fss, ts, xs, Xs, f_s): # Define plots _, axes = plt.subplots(nrows=len(fss), ncols=2, figsize=(15, 6)) for i, fs in enumerate(fss): t = ts[i] x = xs[i] X = Xs[i] f = f_s[i] # Plot results axes[i, 0].plot(t, x, "-*") axes[i, 0].set_title(f"x(t) with $f_s={fs}$Hz") axes[i, 0].set_xlabel("time [s]") axes[i, 1].stem(f, np.abs(X)) axes[i, 1].set_title(f"X(f) with $f_s={fs}$Hz") axes[i, 1].set_xlabel("Frequency [Hz]") plt.tight_layout() plt.show() def plot_1_5(sigmas, t, f, xns, Xns): _, axes = plt.subplots(nrows=len(sigmas), ncols=2, figsize=(15, 10)) for i, sigma in enumerate(sigmas): xn = xns[i] Xn = Xns[i] # Time-domain plot axes[i, 0].plot(t, xn) axes[i, 0].set_xlabel("Time [s]") axes[i, 0].set_title(f"Temporal ($\\sigma={sigma}$)") # Frequency-domain plot axes[i, 1].stem(f, np.abs(Xn)) axes[i, 1].set_xlabel("Frequency [Hz]") axes[i, 1].set_title(f"Fourier transform ($\\sigma={sigma}$)") plt.tight_layout() plt.show() def plot_2_2(xs, Xs, t, f): _, axes = plt.subplots(nrows=len(xs), ncols=2, figsize=(16, 10)) for i, (x, X) in enumerate(zip(xs, Xs)): # Time-domain plot axes[i, 0].plot(t, x) axes[i, 0].set_title(f"$x_{{{i+1}}}(t)$") axes[i, 0].set_xlabel("Time [s]") # Frequency-domain plot axes[i, 1].plot(f, np.abs(X)) axes[i, 1].set_title(f"$|X_{{{i+1}}}(f)|$") axes[i, 1].set_xlabel("Frequency [Hz]") plt.tight_layout() plt.show() def plot_3(Bs, t, pis): for B, pi in zip(Bs, pis): plt.plot(t, pi, label=f"B={B}") plt.legend() plt.title("Function $\\Pi(t/B)$") plt.xlabel("Time [s]") plt.show() def plot_4(Ks, t, x, x_hats, K_error, errs): _, axes = plt.subplots(1, 3, figsize=(15, 5)) # Base function axes[0].plot(t, x(t), c='k', linewidth=3, label='$x(t)$') axes[0].set_title('$x(t)$') axes[0].set_xlabel('Time [s]') axes[0].legend() # Approximations axes[1].plot(t, x(t), c='k', linewidth=3, label='$x(t)$') for K, x_hat in zip(Ks, x_hats): axes[1].plot(t, x_hat, label='$\\hat{{x}}(t)$, $k={}$'.format(K), linewidth=2) axes[1].set_title('Approximation - Chebyshev') axes[1].set_xlabel('Time [s]') axes[1].legend() # Error vs number of coefficients axes[2].semilogy(K_error, errs, label='error = $||x - \\hat{x}||^2$') axes[2].set_title('Reconstruction error') axes[2].set_ylabel('Error') axes[2].set_xlabel('K') axes[2].legend() plt.tight_layout() plt.show() def plot_5_2(t, Sn): fig, ax = plt.subplots(figsize=(15, 4)) for i in range(Sn.shape[0]): ax.plot(t, Sn[i], label=f"$s_{i}(t)$") ax.set_title("$s_n(t)$") ax.set_xlabel("time t") ax.legend() plt.show() def plot_5_2_2(t, Phi): fig, ax = plt.subplots(figsize=(15, 4)) for i in range(Phi.shape[0]): ax.plot(t, Phi[i], label=fr"$\phi_{{{i}}}(t)$") ax.set_title(r"$\phi_n(t)$") ax.set_xlabel("Time [s]") ax.legend() plt.show() def plot_5_3(t, S, B): fig, axes = plt.subplots(1, 2, figsize=(15, 4)) for i in range(S.shape[0]): axes[0].plot(t, S[i], label=fr"$s_{{{i}}}(t)$") for i in range(B.shape[0]): axes[1].plot(t, B[i], label=fr"$\phi_{{{i}}}(t)$") axes[0].set_xlabel("time [s]") axes[0].set_title(r"$s_n(t)$") axes[1].set_xlabel("time [s]") axes[1].set_title(r"$\phi_n(t)$") for a in axes: a.legend() plt.show() def plot_5_proj(t, f, Ks, f_hats, mses): fig, axes = plt.subplots(1, 2, figsize=(15, 5)) axes[0].plot(t, f, label=r"$f(t)$", linewidth=2) for K, fk in zip(Ks, f_hats): axes[0].plot(t, fk, linestyle="--", label=fr"$\hat{{f}}_K(t)$, $K={K}$") axes[0].set_title(r"Projection sur la base $\{\phi_n\}$") axes[0].set_xlabel("time [s]") axes[0].legend() axes[1].plot(Ks, mses, marker="*") axes[1].set_xlabel("K") axes[1].set_ylabel("MSE") axes[1].set_title("Erreur de reconstruction (MSE) vs K") plt.tight_layout() plt.show() def plot_6(t, f, x_real, x_imag, X_real, X_imag): fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(15, 8)) axes[0].plot(t, x_real, label="real") axes[0].plot(t, x_imag, label="imag") axes[0].set_title(r"Temporal signal $x(t)$") axes[0].set_xlabel("Time [s]") axes[0].legend(loc=1) axes[1].stem(f, X_real, label="real") axes[1].set_ylim([-0.3, 0.3]) axes[1].set_title("FFT Real part") axes[1].set_xlabel("Frequency [Hz]") axes[2].hlines(3/16, xmin=f[0], xmax=f[-1], ls='--', color='k', label=r"$j\frac{3}{16}$") axes[2].hlines(1/16, xmin=f[0], xmax=f[-1], ls='-.', color='k', label=r"$j\frac{1}{16}$") axes[2].stem(f, X_imag, label="imag") axes[2].set_ylim([-0.3, 0.3]) axes[2].set_title("FFT Imaginary part") axes[2].set_xlabel("Frequency [Hz]") axes[2].legend(loc=1) plt.tight_layout() plt.show()