#!/usr/bin/env python3 # coding: utf8 # Interface graphique pour illustrer la convolution # Licence libre WTFPL import tkinter import numpy as np from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg from matplotlib.figure import Figure from matplotlib.pyplot import tight_layout # Définition des signaux############################################# Fe = 1e4 # approximation continue N = 2*Fe # nombre de points jusqu'à +- 1s n = np.arange(-(N/2), N/2) t = n / Fe T = 1/3 # taille de la porte fBF = 4 # basse fréquence du sinus fHF = 48 # haute fréquence du sinus t0 = 1/20 # paramètre de l'exponentielle miny = 0.01 # minimum d'axe vertical res_tau = 0.005 # résolution du slider de temps dirac = np.zeros(t.shape) dirac[t == 0] = 1 dirdec = np.zeros(t.shape) dirdec[t == 0.1] = 1 por = np.zeros(t.shape) por[np.abs(t) < T/2] = 1 porcaus = np.zeros(t.shape) porcaus[t < T/2] = 1 porcaus[t < 0] = 0 expo = np.exp(-t / t0) * (t >= 0) # exponentielle causale expo = expo/np.sum(expo)*Fe # pour équivalent de tension 1V avec porte axef = np.arange(N)/N*Fe - Fe/2 # axe fréquentiel fc = (fBF + fHF) / 2 # fréquence de coupure idéale filtre = abs(axef) < fc rifiltre = np.real(np.fft.fftshift(np.fft.ifft(np.fft.fftshift(filtre))))*por rifiltre = rifiltre*Fe # normalisation pour affichage sympa sinBF = np.sin(2*np.pi*fBF*t) sinHF = np.sin(2*np.pi*fHF*t) # dictionnaire des signaux dic_signals = {} dic_signals["dirac"] = dirac dic_signals["dirac retardé"] = dirdec dic_signals["porte"] = por dic_signals["porte causale"] = porcaus dic_signals["r.i. exponentielle"] = expo dic_signals["sinus cardinal tronq"] = rifiltre dic_signals["sinus basse fréq"] = sinBF dic_signals["sinus haute fréq"] = sinHF list_signals = ["dirac", "dirac retardé", "porte", "porte causale", "r.i. exponentielle", "sinus cardinal tronq", "sinus basse fréq", "sinus haute fréq"] # Classe de base ##################################################### class Convolution: def __init__(self, t, dic_signals, list_signals): # Initialisation des données # self.t = t self.dic_signals = dic_signals self.list_signals = list_signals self.sig1 = self.dic_signals["dirac"] self.sig2 = self.dic_signals["dirac"] self.fd1 = True # flag a-t-on un dirac en signal 1 ? self.fd2 = True # idem signal 2 self.tau = 0 # Initialisation de l'affichage # self.root = tkinter.Tk() self.root.wm_title("Étude de la convolution") # Défaut en plein écran # xmax = self.root.winfo_screenwidth() ymax = self.root.winfo_screenheight()-20 self.root.geometry(str(xmax) + "x" + str(ymax) + "+0+0") self.fig = Figure() self.a1 = self.fig.add_subplot(411) self.a2 = self.fig.add_subplot(412) self.a3 = self.fig.add_subplot(413) self.a4 = self.fig.add_subplot(414) self.fig.subplots_adjust() menu_width = 150 self.canvas = FigureCanvasTkAgg(self.fig, master=self.root) self.canvas.get_tk_widget().place(width=xmax-menu_width, height=ymax) self.canvas.mpl_connect("key_press_event", self.key_bindings) # Création des widgets # self.frame = tkinter.Frame(self.root, width=0.5) self.frame.place(x=xmax-menu_width, width=menu_width, height=ymax) self.scale_tau = tkinter.Scale(master=self.frame, orient='horizontal', from_=-0.5, to=0.5, resolution=res_tau, length=menu_width-20, command=self.change_tau) self.scale_tau.set(self.tau) labeltau = tkinter.Label(self.frame, text="valeur de t") labeltau.place(rely=0.83, x=30) self.scale_tau.place(rely=0.83, x=10, y=20) # 20 : taille du label # Création des menus de choix de signaux # self.x = tkinter.StringVar() self.choix_x = tkinter.OptionMenu(self.frame, self.x, *self.list_signals, command=self.change_x) self.x.set(self.list_signals[0]) labelx = tkinter.Label(self.frame, text="signal x(t)") labelx.place(rely=0.1, x=10) self.choix_x.place(rely=0.1, x=5, y=20) # 20 : taille du label self.y = tkinter.StringVar() self.choix_y = tkinter.OptionMenu(self.frame, self.y, *self.list_signals, command=self.change_y) self.y.set(self.list_signals[0]) labely = tkinter.Label(self.frame, text="signal y(t)") labely.place(rely=0.3, x=10) self.choix_y.place(rely=0.3, x=5, y=20) # 20 : taille du label # Affichage initial # self.affiche() self.fig.tight_layout() # répétition de affiche() self.canvas.draw() # pour initialiser correctement # callback des différents choix # def change_tau(self, tau): self.tau = float(tau) self.affiche() def change_x(self, signal): self.sig1 = self.dic_signals[self.x.get()] if signal in ["dirac", "dirac retardé"]: self.fd1 = 1 else: self.fd1 = 0 self.affiche() def change_y(self, signal): self.sig2 = self.dic_signals[self.y.get()] if signal in ["dirac", "dirac retardé"]: self.fd2 = 1 else: self.fd2 = 0 self.affiche() # fonction d'affichage # def affiche(self): self.affiche1() self.affiche2() self.affiche3() self.affiche4() self.fig.tight_layout() self.canvas.draw() def affiche1(self): self.a1.clear() tmp = self.a1.plot(self.t, self.sig1, linewidth=2) if self.fd1: nd = self.sig1.argmax() - (self.t == 0).argmax() self.a1.plot(((nd-100)/Fe, nd/Fe), (0.8, 1), color=tmp[0].get_color(), linewidth=2) self.a1.plot((nd/Fe, (nd+100)/Fe), (1, 0.8), color=tmp[0].get_color(), linewidth=2) self.a1.set_xlim((-0.5, 0.5)) ymax = max(max(abs(self.sig1)), miny) self.a1.set_ylim((-1.1*ymax, 1.1*ymax)) self.a1.set_title('x(u)') self.a1.grid("on") self.a1.set_ylabel('amplitude') self.a1.set_xlabel('temps u') def affiche2(self): self.a2.clear() tmp = self.a2.plot(self.t, self.sig2, linewidth=2) tmpt = self.a2.plot(self.t+self.tau, self.sig2[::-1], linewidth=2) if self.fd2: nd = self.sig2.argmax() - (self.t == 0).argmax() self.a2.plot(((nd-100)/Fe, nd/Fe), (0.8, 1), color=tmp[0].get_color(), linewidth=2) self.a2.plot((nd/Fe, (nd+100)/Fe), (1, 0.8), color=tmp[0].get_color(), linewidth=2) nd = self.sig2[::-1].argmax() - ((self.t+self.tau) == 0).argmax() self.a2.plot(((nd-100)/Fe, nd/Fe), (0.8, 1), color=tmpt[0].get_color(), linewidth=2) self.a2.plot((nd/Fe, (nd+100)/Fe), (1, 0.8), color=tmpt[0].get_color(), linewidth=2) self.a2.set_xlim((-0.5, 0.5)) self.a2.set_xlim((-0.5, 0.5)) ymax = max(max(abs(self.sig2)), miny) self.a2.set_ylim((-1.1*ymax, 1.1*ymax)) self.a2.set_title('y(u) et y(t-u)') self.a2.grid("on") self.a2.set_ylabel('amplitude') self.a2.set_xlabel('temps u') def affiche3(self): ntau = np.round(self.tau*Fe) s1 = self.sig1[np.abs(n) < (Fe/2)] s2 = self.sig2[np.abs(n - ntau) < (Fe/2)][::-1] # equivalent to abs(t+tau) < 0.5, without round errors axet = self.t[abs(self.t) < 0.5] self.a3.clear() tmp = self.a3.plot(axet, s1*s2, linewidth=2) if self.fd1 or self.fd2: nd = abs(s1*s2).argmax() - (axet == 0).argmax() ampl = (s1*s2)[s1*s2 != 0] if ampl.size > 0: self.a3.plot(((nd-100)/Fe, nd/Fe), (0.8*ampl, ampl), color=tmp[0].get_color(), linewidth=2) self.a3.plot((nd/Fe, (nd+100)/Fe), (ampl, 0.8*ampl), color=tmp[0].get_color(), linewidth=2) self.a3.fill_between(axet, 0, s1*s2, color="green", alpha=0.2) self.a3.set_xlim((-0.5, 0.5)) ymax = max(max(abs(s1*s2)), miny) self.a3.set_ylim((-1.1*ymax, 1.1*ymax)) self.a3.set_title('x(u) × y(t-u)') self.a3.grid("on") self.a3.set_ylabel('amplitude') self.a3.set_xlabel('temps u') def affiche4(self): self.a4.clear() r = np.convolve(self.sig1, self.sig2, mode="full") lags = np.arange(-len(self.sig1)+1, len(self.sig1)) if not(self.fd1) and not(self.fd2): # pas d'élément neutre r = r/Fe # normalisation pour le continu tmp = self.a4.plot(lags/Fe, r, linewidth=2) ymax = max(max(r), miny) ymin = -ymax self.a4.plot((self.tau, self.tau), (1.5*ymin, 1.5*ymax), color='r', linewidth=2) if self.fd1 and self.fd2: nd = r.argmax() - (lags == 0).argmax() self.a4.plot(((nd-100)/Fe, nd/Fe), (0.8, 1), color=tmp[0].get_color(), linewidth=2) self.a4.plot((nd/Fe, (nd+100)/Fe), (1, 0.8), color=tmp[0].get_color(), linewidth=2) self.a4.set_xlim((-0.5, 0.5)) self.a4.set_ylim((1.2*ymin, 1.2*ymax)) self.a4.set_title(r'$z(t) = x(t)*y(t) = \int x(u)y(t-u)du$') self.a4.grid("on") self.a4.set_ylabel('amplitude') self.a4.set_xlabel('temps t') def key_bindings(self, event): if event.key in ["x"]: # x(t) suivant idx = self.list_signals.index(self.x.get()) new_idx = (idx + 1) % len(self.list_signals) self.x.set(self.list_signals[new_idx]) self.change_x(self.list_signals[new_idx]) if event.key in ["X"]: # x(t) précédent idx = self.list_signals.index(self.x.get()) new_idx = (idx - 1) % len(self.list_signals) self.x.set(self.list_signals[new_idx]) self.change_x(self.list_signals[new_idx]) if event.key in ["y"]: # y(t) suivant idx = self.list_signals.index(self.y.get()) new_idx = (idx + 1) % len(self.list_signals) self.y.set(self.list_signals[new_idx]) self.change_y(self.list_signals[new_idx]) if event.key in ["Y"]: # y(t) précédent idx = self.list_signals.index(self.y.get()) new_idx = (idx - 1) % len(self.list_signals) self.y.set(self.list_signals[new_idx]) self.change_y(self.list_signals[new_idx]) if event.key in ["q", "Q"]: # quitter self.root.quit() self.root.destroy() if event.key in ["left"]: # diminuer τ self.scale_tau.set(self.tau-res_tau) if event.key in ["right"]: # augmenter τ self.scale_tau.set(self.tau+res_tau) if event.key in ["ctrl+left"]: # plus diminuer τ self.scale_tau.set(self.tau-10*res_tau) if event.key in ["ctrl+right"]: # plus augmenter τ self.scale_tau.set(self.tau+10*res_tau) conv = Convolution(t, dic_signals, list_signals) tkinter.mainloop()