#!/usr/bin/env python3 # coding: utf8 # Interface graphique pour illustrer la corrélation # 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 # résolution de τ res_tau = 0.005 # 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 des porte et triangle f = 13 # fréquence des sinus et cosinus por = np.zeros(t.shape) por[np.abs(t) < T/2] = 1 tri = 1 - np.abs(t) / (T/2) tri[tri < 0] = 0 cosin = np.cos(2*np.pi*f*t) sinus = np.sin(2*np.pi*f*t) # séquence SBPA précréée sbpa = np.hstack((np.ones(10), -np.ones(7), np.ones(3), -np.ones(4), 1)) # on répète ces points par un facteur donné pour être visible # et on remet ça en ligne fac = 50 seq = np.array([i*np.ones(50) for i in sbpa]) seq = np.reshape(seq, -1) ex1 = np.zeros(t.shape) ex2 = np.zeros(t.shape) n0 = int(np.where(t == 0)[0]) n1 = int(np.where(t == 0.25)[0]) seqlen = int(len(seq)) ex1[n0:n0+seqlen] = seq ex2[n1:n1+seqlen] = seq # dictionnaire des signaux dic_signals = {} dic_signals["porte"] = por dic_signals["triangle"] = tri dic_signals["cosinus"] = cosin dic_signals["sinus"] = sinus dic_signals["cosinus fini"] = cosin*por dic_signals["sinus fini"] = sinus*por dic_signals["signal test"] = ex1 dic_signals["test retardé"] = ex2 list_signals = ["porte", "triangle", "cosinus", "sinus", "cosinus fini", "sinus fini", "signal test", "test retardé"] # Classe de base ##################################################### class Correlation: 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["porte"] self.sig2 = self.dic_signals["porte"] self.tau = 0 self.list_rsb = ["10 dB", "3 dB", "0 dB", "-3 dB", "-10 dB"] # Initialisation de l'affichage # self.root = tkinter.Tk() self.root.wm_title("Étude de la corrélation") # 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 = 120 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="retard τ") 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 # Gestion du bruit self.bruit = tkinter.IntVar() self.check_bruit = tkinter.Checkbutton(master=self.frame, text="Signal bruité", variable=self.bruit, onvalue=True, offvalue=False, command=self.ajoute_bruit) self.check_bruit.place(rely=0.4, x=5) self.bruit.set(False) self.rsb = tkinter.StringVar() self.choix_rsb = tkinter.OptionMenu(self.frame, self.rsb, *self.list_rsb, command=self.change_rsb) self.rsb.set(self.list_rsb[0]) # il faut supprimer « dB » à la fin et conversion linéaire self.rsb_lin = 10**(float(self.list_rsb[0].split()[0])/10) self.labelrsb = tkinter.Label(self.frame, text="RSB") # placement fait uniquement lorsque « signal bruité » est coché # → dans self.ajoute_bruit self.memebruit = tkinter.IntVar() self.meme_bruit = tkinter.Checkbutton(master=self.frame, text="Même bruit", variable=self.memebruit, onvalue=True, offvalue=False, command=self.ajoute_bruit) self.memebruit.set(False) self.pointzero = tkinter.IntVar() self.point_zero = tkinter.Checkbutton(master=self.frame, text="Point central", variable=self.pointzero, onvalue=True, offvalue=False, command=self.affiche) self.pointzero.set(True) # 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()] self.bruite() def change_y(self, signal): self.sig2 = self.dic_signals[self.y.get()] self.bruite() def bruite(self): if self.bruit.get(): bruit = np.random.randn(len(self.sig1))/self.rsb_lin else: bruit = 0 self.sig1 = self.dic_signals[self.x.get()] + bruit if self.bruit.get() and not self.memebruit.get(): bruit = np.random.randn(len(self.sig1))/self.rsb_lin self.sig2 = self.dic_signals[self.y.get()] + bruit self.affiche() def ajoute_bruit(self): if self.bruit.get(): self.meme_bruit.place(rely=0.45, x=5) self.labelrsb.place(rely=0.5, x=10) self.choix_rsb.place(rely=0.5, x=5, y=20) # 20 : taille du label if self.memebruit.get(): self.point_zero.place(rely=0.75, x=5) else: self.point_zero.place_forget() else: self.meme_bruit.place_forget() self.labelrsb.place_forget() self.choix_rsb.place_forget() self.point_zero.place_forget() self.bruite() def change_rsb(self, data): # il faut supprimer « dB » à la fin et conversion linéaire self.rsb_lin = 10**(float(data.split()[0])/10) self.bruite() # 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() self.a1.plot(self.t, self.sig1, linewidth=2) self.a1.set_xlim((-0.5, 0.5)) maxy = np.max(self.sig1) miny = np.min(self.sig1) self.a1.set_ylim((1.1*miny, 1.1*maxy)) self.a1.set_title('x(t)') self.a1.grid("on") self.a1.set_ylabel('amplitude') self.a1.set_xlabel('temps t') def affiche2(self): self.a2.clear() self.a2.plot(self.t+self.tau, self.sig2, linewidth=2) self.a2.set_xlim((-0.5, 0.5)) maxy = np.max(self.sig2) miny = np.min(self.sig2) self.a2.set_ylim((1.1*miny, 1.1*maxy)) self.a2.set_title(r'$y(t-\tau)$') self.a2.grid("on") self.a2.set_ylabel('amplitude') self.a2.set_xlabel('temps t') 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)] # equivalent to abs(t+tau) < 0.5, without round errors axet = self.t[abs(self.t) < 0.5] self.a3.clear() self.a3.plot(axet, s1*s2, linewidth=2) self.a3.fill_between(axet, 0, s1*s2, color="green", alpha=0.2) self.a3.set_xlim((-0.5, 0.5)) maxy = np.max(s1*s2) miny = np.min(s1*s2) self.a3.set_ylim((1.1*miny, 1.1*maxy)) self.a3.set_title(r'$x(t) \times y(t-\tau)$') self.a3.grid("on") self.a3.set_ylabel('amplitude') self.a3.set_xlabel('temps t') def affiche4(self): self.a4.clear() r = np.correlate(self.sig1, self.sig2, mode="full") lags = np.arange(-len(self.sig1)+1, len(self.sig1)) r = r/Fe # normalisation pour le continu if self.memebruit.get() and not self.pointzero.get(): r[lags == 0] = None self.a4.plot(lags/Fe, r, linewidth=2) self.a4.plot((self.tau, self.tau), (1.5*min(r), 1.5*max(r)), color='r', linewidth=2) self.a4.set_xlim((-0.5, 0.5)) self.a4.set_ylim((1.1*min(r), 1.1*max(r))) self.a4.set_title(r'$\gamma_{xy}(\tau) = \int x(t)y(t-\tau)dt$') self.a4.grid("on") self.a4.set_ylabel('amplitude') self.a4.set_xlabel(r'retard $\tau$') 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) corr = Correlation(t, dic_signals, list_signals) tkinter.mainloop()