-
Notifications
You must be signed in to change notification settings - Fork 4
/
Demo_1_example_simulation.m
172 lines (158 loc) · 6.67 KB
/
Demo_1_example_simulation.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
% Copyright (c) 2021 Mohammad Fathi Al-Sa'd
%
% Permission is hereby granted, free of charge, to any person obtaining a
% copy of this software and associated documentation files (the "Software"),
% to deal in the Software without restriction, including without limitation
% the rights to use, copy, modify, merge, publish, distribute, sublicense,
% and/or sell copies of the Software, and to permit persons to whom the
% Software is furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included
% in all copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
% OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
% THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
% DEALINGS IN THE SOFTWARE.
%
% Email: mohammad.al-sad@tuni.fi, alsad.mohamed@gmail.com
%
% The following reference should be cited whenever this script is used:
% M. Al-Sa'd, B. Boashash, M. Gabbouj, "Design of an Optimal Piece-Wise
% Spline Wigner-Ville Distribution for TFD Performance Evaluation and
% Comparison", IEEE Transactions on Signal Processing, 2021.
%
% Last Modification: 12-March-2021
%
% Description:
% This demo script produces the results that are depicted in Fig. 2 of the
% paper. It generates an example 2-component non-stationary signal and
% computes its PW-WVD, WVD and the WVD cross-terms. In addition, it shows
% the signal IA, IF, and time-support functions.
%% Initialization
clear; close all; clc;
addpath(genpath('Functions'));
%% Parameters
N = 256;
M = 256;
fs = 1;
t = 0:1/fs:(N-1)/fs;
f = 0:fs/(2*N-1):fs/2;
C_max = 50;
%% Generate component 1
pt = [20 80 130 180 230]';
pf = [0.4 0.2 0.35 0.15 0.3]';
w = (t >= min(pt) & t <= max(pt));
R = length(pt) - 1;
tif = zeros(N,R+1);
tif(:,end) = ones(N,1);
for r = 1:R
tif(:,r) = t.^(R-r+1);
end
tip = [(t.^(R+1))' tif(:,1:R)]./((R+1):-1:1);
RR = repmat(R:-1:0,R+1,1);
A = pt.^RR;
C = A\pf;
IF(1,:) = (tif*C)';
IP(1,:) = (tip*C)';
IA(1,:) = exp(-0.008*t);
W(1,:) = w;
z(1,:) = IA(1,:).*exp(1j*2*pi*IP(1,:)).*W(1,:);
%% Generate component 2
pt = [100 220]';
pf = [0.05 0.4]';
w = (t >= min(pt) & t <= max(pt));
R = length(pt) - 1;
tif = zeros(N,R+1);
tif(:,end) = ones(N,1);
for r = 1:R
tif(:,r) = t.^(R-r+1);
end
tip = [(t.^(R+1))' tif(:,1:R)]./((R+1):-1:1);
RR = repmat(R:-1:0,R+1,1);
A = pt.^RR;
C = A\pf;
IF(2,:) = (tif*C)';
IP(2,:) = (tip*C)';
IA(2,:) = 0.4 + 0.3.*cos(0.01*pi*t);
W(2,:) = w;
z(2,:) = IA(2,:).*exp(1j*2*pi*IP(2,:)).*W(2,:);
%% PW-WVD (Lz)
Lz = pw_wvd(IF,IP,IA,W,fs);
%% WVD (Wz)
Wz = qtfd_wvd(sum(z),N-1);
%% WVD cross-terms (Xz)
Xz = Lz - Wz;
%% Plotting IA laws
figure('Color',[1,1,1],'Position',[100 100 650 550]);
plot(t,IA(1,:),'b','linewidth',3); hold on;
plot(t,IA(2,:),'r','linewidth',3); hold on;
legend('$$a_1(t)$$','$$a_2(t)$$','Interpreter','LaTeX','location',...
'northeast','fontsize',30,'FontName','Times','orientation','horizontal',...
'Position',[0.18420512453715 0.827878790479718 0.411382203954988 0.0945454519445246]);
grid on; axis([t(1) t(end) 0 1.05]);
xlabel('Time (s)'); ylabel('Amplitude');
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Plotting IF laws
figure('Color',[1,1,1],'Position',[100 100 650 550]);
plot(IF(1,:),t,'b','linewidth',3); hold on;
plot(IF(2,:),t,'r','linewidth',3); hold on;
legend('$$f_1(t)$$','$$f_2(t)$$','Interpreter','LaTeX','location',...
'northeast','fontsize',30,'FontName','Times','orientation','horizontal',...
'Position',[0.18420512453715 0.827878790479718 0.411382203954988 0.0945454519445246]);
grid on; axis([f(1) f(end) t(1) t(end)]);
xlabel('Frequency (Hz)'); ylabel('Time (s)');
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Plotting Windows
figure('Color',[1,1,1],'Position',[100 100 650 550]);
plot(t,W(1,:),'b','linewidth',3); hold on;
plot(t,W(2,:),'r','linewidth',3); hold on;
legend('$$\Pi_1(t)$$','$$\Pi_2(t)$$','Interpreter','LaTeX','location',...
'northeast','fontsize',30,'FontName','Times','orientation','horizontal',...
'Position',[0.18420512453715 0.827878790479718 0.411382203954988 0.0945454519445246]);
grid on; axis([t(1) t(end) -0.05 1.19]);
xlabel('Time (s)'); ylabel('Amplitude');
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Plotting Lz
figure('Color',[1,1,1],'Position',[100 100 650 550]);
colormap(1-gray); imagesc(f,t,abs(Lz)); axis xy;
xlabel('Frequency (Hz)'); ylabel('Time (s)');
axis([f(1) f(end) t(1) t(end)]); caxis([0 C_max]);
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Plotting Wz
figure('Color',[1,1,1],'Position',[100 100 650 550]);
colormap(1-gray); imagesc(f,t,abs(Wz)); axis xy;
xlabel('Frequency (Hz)'); ylabel('Time (s)');
axis([f(1) f(end) t(1) t(end)]); caxis([0 C_max]);
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Plotting Xz
figure('Color',[1,1,1],'Position',[100 100 650 550]);
colormap(1-gray); imagesc(f,t,abs(Xz)); axis xy;
xlabel('Frequency (Hz)'); ylabel('Time (s)');
axis([f(1) f(end) t(1) t(end)]); caxis([0 C_max]);
set(gca,'fontweight','bold','fontsize',24,'FontName','Times');
set(gcf,'Units','inches'); screenposition = get(gcf,'Position');
set(gcf,'PaperPosition',[0 0 screenposition(3:4)],'PaperSize',screenposition(3:4));
%% Saving
opt = input('Do you want to save all results (Y/N)\n','s');
if(opt == 'y' || opt == 'Y')
print(1,'IA','-dpdf','-r400');
print(2,'IF','-dpdf','-r400');
print(3,'IW','-dpdf','-r400');
print(4,'Lz','-dpdf','-r400');
print(5,'Wz','-dpdf','-r400');
print(6,'Xz','-dpdf','-r400');
end