常见窗函数的幅度谱、相位谱（DTFT）
作者：互联网
昨天手机弹窗新闻，日本前首相安倍街头演讲时遇刺，“百年未有之大变局”……
继续做题。
一、 在数字信号处理（DSP）中非常有用的四种有限长序列，也称为窗函数。将各自幅度谱归一化（即幅度最大值为1），然后画出图形。
二、上代码
1 // Book Author:Vinay K Ingle, John G Proakis
2 //
3 // Problem 3.4
4 // script by: KY
5 //
6 clear, clc, clf();
7
8 mode(2);
9 funcprot(0);
10 load('../fun/lib');
11
12 // -----------------------------------------------------------------------------
13 // START Output Info about this sce-file
14 mprintf('\n***********************************************************\n');
15 [ban1,ban2] = fun_banner();
16 mprintf("\n <DSP using MATLAB> 3rd edition, Problem 3.4 \n");
17 mprintf(" ----------------------------------------------------------\n\n");
18
19 // ----------------END----------------------------------------------------------
20
21
22 //% ----------------------------------------------
23 //% Rectangle Window sequence
24 //% ----------------------------------------------
25 M = 101;
26
27 n1_start = 0; n1_end = M;
28 n1 = [n1_start : n1_end - 1];
29
30 x1 = ones(1, length(n1));
31
32 // -----------------------------------------------------------------------------
33 // --------------------START f0 figure-----------------------------------------
34 f0=scf(0); //creates figure with id==0 and make it the current one
35 f0.figure_size=[1000,700]; // adjust window size
36 f0.background=8; // add background color 8-white
37 f0.figure_name="Problem 3.4 Rectangle"; // name window
38 subplot(1, 1, 1);
39
40 plot(n1,x1,'bo');
41 plot(n1,x1,'b.');
42 plot2d3(n1,x1,2); // Create plot with blue line
43 title("$x1(n)\ Rectangle\ sequence$",'fontname',7,'fontsize',4);
44 //title("mprintf('x1(n) sequence, M = %d', M)");
45 xlabel('$n$','fontname',3); ylabel('x1(n)','fontname',3,'fontsize',3);
46 xgrid(5,0,7); // color, thickness, style
47 a0=get("current_axes"); // get the handle of the newly created axes
48 //a0.data_bounds=[-4,6,-6,6];
49 // -----------------------------------------------------------------------------
50 // --------------------END f0 -------------------------------------------------
51
52
53 MM = 500;
54 k = [-MM:MM]; // [-pi, pi]
55 //k = [0:M]; // [0, pi]
56 w = (%pi/MM) * k;
57
58 [X1] = fun_dtft(x1, n1, w);
59
60 magX1 = abs(X1); angX1 = fun_angle(X1); realX1 = real(X1); imagX1 = imag(X1);
61
62 //%% ---------------------------------------------------------------------------
63 //%% START X(w)'s mag ang real imag
64 // --------------------START f1 figure-----------------------------------------
65 f1=scf(1); //creates figure with id==0 and make it the current one
66 f1.figure_size=[1000,700]; // adjust window size
67 f1.background=8; // add background color 8-white
68 f1.figure_name="Problem 3.4 DTFT of Rm(n)"; // name window
69 subplot(2, 1, 1);
70 plot(w/%pi,magX1/max(magX1));
71 title("$Magnitude\ Response$",'fontname',7,'fontsize',4);
72 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('Magnitude |X|','fontname',3,'fontsize',3);
73 xgrid(5,0,7); // color, thickness, style
74 a0=get("current_axes"); // get the handle of the newly created axes
75 //a0.data_bounds=[-4,6,-6,6];
76
77 subplot(2, 1, 2);
78 plot(w/%pi,angX1/%pi*exp(0));
79 title("$Phase\ Response$",'fontname',7,'fontsize',4);
80 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('$Radians/\pi*exp(0)$','fontname',3,'fontsize',3);
81 xgrid(5,1,7); // color, thickness, style
82 a1=get("current_axes"); // get the handle of the newly created axes
83 //a1.data_bounds=[-4,6,-2,2];
84 // ----------------------------END f1-------------------------------------------
85 //%% END X(w)'s mag ang real imag
86 //%% ---------------------------------------------------------------------------
87
88
89 //% --------------------------------------------------
90 //% Hanning Window Sequence
91 //% --------------------------------------------------
92 //n2_start = -9; n2_end = 15;
93 //n2 = [n2_start : n2_end];
94 n2 = n1;
95 x2 = 0.5 * (1 - cos(2*%pi*n1/(M-1))) .* x1;
96
97 // -----------------------------------------------------------------------------
98 // --------------------START f2 figure-----------------------------------------
99 f2=scf(2); //creates figure with id==0 and make it the current one
100 f2.figure_size=[1000,700]; // adjust window size
101 f2.background=8; // add background color 8-white
102 f2.figure_name="Problem 3.4 x2(n) Hanning"; // name window
103 subplot(1, 1, 1);
104
105 plot(n2,x2,'bo');
106 plot(n2,x2,'b.');
107 plot2d3(n2,x2,2); // Create plot with blue line
108 title("$x2(n)\ Hanning\ sequence$",'fontname',7,'fontsize',4);
109 //title(mprintf('x1(n) sequence, M = %d', M));
110 xlabel('$n$','fontname',3); ylabel('x2(n)','fontname',3,'fontsize',3);
111 xgrid(5,0,7); // color, thickness, style
112 a0=get("current_axes"); // get the handle of the newly created axes
113 //a0.data_bounds=[-4,6,-6,6];
114 // -----------------------------------------------------------------------------
115 // --------------------END f2 -------------------------------------------------
116
117
118 MM = 500;
119 k = [-MM:MM]; // [-pi, pi]
120 //k = [0:M]; // [0, pi]
121 w = (%pi/MM) * k;
122
123 [X2] = fun_dtft(x2, n2, w);
124
125 magX2 = abs(X2); angX2 = fun_angle(X2); realX2 = real(X2); imagX2 = imag(X2);
126
127 //%% ---------------------------------------------------------------------------
128 //%% START X(w)'s mag ang real imag
129 // --------------------START f3 figure-----------------------------------------
130 f3=scf(3); //creates figure with id==0 and make it the current one
131 f3.figure_size=[1000,700]; // adjust window size
132 f3.background=8; // add background color 8-white
133 f3.figure_name="Problem 3.4 DTFT of Cm(n)"; // name window
134 subplot(2, 1, 1);
135 plot(w/%pi,magX2/max(magX2));
136 title("$Magnitude\ Response$",'fontname',7,'fontsize',4);
137 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('Magnitude |X|','fontname',3,'fontsize',3);
138 xgrid(5,0,7); // color, thickness, style
139 a0=get("current_axes"); // get the handle of the newly created axes
140 //a0.data_bounds=[-4,6,-6,6];
141
142 subplot(2, 1, 2);
143 plot(w/%pi,angX2/%pi*exp(0));
144 title("$Phase\ Response$",'fontname',7,'fontsize',4);
145 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('$Radians/\pi*exp(0)$','fontname',3,'fontsize',3);
146 xgrid(5,1,7); // color, thickness, style
147 a1=get("current_axes"); // get the handle of the newly created axes
148 //a1.data_bounds=[-4,6,-2,2];
149 // ----------------------------END f3-------------------------------------------
150 //%% END X(w)'s mag ang real imag
151 //%% ---------------------------------------------------------------------------
152
153
154 //% --------------------------------------------------
155 //% Triangular Window Sequence
156 //% --------------------------------------------------
157 //n3_start = -3; n3_end = 10;
158 //n3 = [n3_start : n3_end];
159 n3 = n1;
160 x3 = (1 - abs(M-1-2*n3)/(M-1)) .* x1;
161
162 // -----------------------------------------------------------------------------
163 // --------------------START f4 figure-----------------------------------------
164 f4=scf(4); //creates figure with id==0 and make it the current one
165 f4.figure_size=[1000,700]; // adjust window size
166 f4.background=8; // add background color 8-white
167 f4.figure_name="Problem 3.4 x3(n) Triangular"; // name window
168 subplot(1, 1, 1);
169
170 plot(n3,x3,'bo');
171 plot(n3,x3,'b.');
172 plot2d3(n3,x3,2); // Create plot with blue line
173 title("$x3(n)\ Triangular\ sequence$",'fontname',7,'fontsize',4);
174 //title(mprintf('x3(n) sequence, M = %d', M));
175 xlabel('$n$','fontname',3); ylabel('x2(n)','fontname',3,'fontsize',3);
176 xgrid(5,0,7); // color, thickness, style
177 a0=get("current_axes"); // get the handle of the newly created axes
178 //a0.data_bounds=[-4,6,-6,6];
179 // -----------------------------------------------------------------------------
180 // --------------------END f4 -------------------------------------------------
181
182 MM = 500;
183 k = [-MM:MM]; // [-pi, pi]
184 //k = [0:M]; // [0, pi]
185 w = (%pi/MM) * k;
186
187 [X3] = fun_dtft(x3, n3, w);
188
189 magX3 = abs(X3); angX3 = fun_angle(X3); realX3= real(X3); imagX3 = imag(X3);
190
191 //%% ---------------------------------------------------------------------------
192 //%% START X(w)'s mag ang real imag
193 // --------------------START f5 figure-----------------------------------------
194 f5=scf(5); //creates figure with id==0 and make it the current one
195 f5.figure_size=[1000,700]; // adjust window size
196 f5.background=8; // add background color 8-white
197 f5.figure_name="Problem 3.4 DTFT of Tm(n)"; // name window
198 subplot(2, 1, 1);
199 plot(w/%pi,magX3/max(magX3));
200 title("$Magnitude\ Response$",'fontname',7,'fontsize',4);
201 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('Magnitude |X|','fontname',3,'fontsize',3);
202 xgrid(5,0,7); // color, thickness, style
203 a0=get("current_axes"); // get the handle of the newly created axes
204 //a0.data_bounds=[-4,6,-6,6];
205
206 subplot(2, 1, 2);
207 plot(w/%pi,angX3/%pi*exp(0));
208 title("$Phase\ Response$",'fontname',7,'fontsize',4);
209 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('$Radians/\pi*exp(0)$','fontname',3,'fontsize',3);
210 xgrid(5,1,7); // color, thickness, style
211 a1=get("current_axes"); // get the handle of the newly created axes
212 //a1.data_bounds=[-4,6,-2,2];
213 // ----------------------------END f5-------------------------------------------
214 //%% END X(w)'s mag ang real imag
215 //%% ---------------------------------------------------------------------------
216
217
218 //% ---------------------------------------------
219 //% Hamming Window sequence
220 //% ---------------------------------------------
221 //n4_start = 0; n4_end = 50;
222 //n4 = [n4_start : n4_end];
223 n4 = n1;
224 x4 = (0.54 - 0.46 * cos(2 * %pi * n4/(M-1))) .* x1;
225
226 // -----------------------------------------------------------------------------
227 // --------------------START f6 figure-----------------------------------------
228 f6=scf(6); //creates figure with id==0 and make it the current one
229 f6.figure_size=[1000,700]; // adjust window size
230 f6.background=8; // add background color 8-white
231 f6.figure_name="Problem 3.4 x4(n) Hamming"; // name window
232 subplot(1, 1, 1);
233
234 plot(n4,x4,'bo');
235 plot(n4,x4,'b.');
236 plot2d3(n4,x4,2); // Create plot with blue line
237 title("$x4(n)\ Hamming\ sequence$",'fontname',7,'fontsize',4);
238 //title(mprintf('x4(n) sequence, M = %d', M));
239 xlabel('$n$','fontname',3); ylabel('x2(n)','fontname',3,'fontsize',3);
240 xgrid(5,0,7); // color, thickness, style
241 a0=get("current_axes"); // get the handle of the newly created axes
242 //a0.data_bounds=[-4,6,-6,6];
243 // -----------------------------------------------------------------------------
244 // --------------------END f6 -------------------------------------------------
245
246
247 MM = 500;
248 k = [-MM:MM]; // [-pi, pi]
249 //k = [0:M]; // [0, pi]
250 w = (%pi/MM) * k;
251
252 [X4] = fun_dtft(x4, n4, w);
253
254 magX4 = abs(X4); angX4 = fun_angle(X4); realX4= real(X4); imagX4 = imag(X4);
255
256 //%% ---------------------------------------------------------------------------
257 //%% START X(w)'s mag ang real imag
258 // --------------------START f7 figure-----------------------------------------
259 f7=scf(7); //creates figure with id==0 and make it the current one
260 f7.figure_size=[1000,700]; // adjust window size
261 f7.background=8; // add background color 8-white
262 f7.figure_name="Problem 3.4 DTFT of Hm(n)"; // name window
263 subplot(2, 1, 1);
264 plot(w/%pi,magX4/max(magX4));
265 title("$Magnitude\ Response$",'fontname',7,'fontsize',4);
266 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('Magnitude |X|','fontname',3,'fontsize',3);
267 xgrid(5,0,7); // color, thickness, style
268 a0=get("current_axes"); // get the handle of the newly created axes
269 //a0.data_bounds=[-4,6,-6,6];
270
271 subplot(2, 1, 2);
272 plot(w/%pi,angX4/%pi*exp(0));
273 title("$Phase\ Response$",'fontname',7,'fontsize',4);
274 xlabel('$frequency\ in\ \pi\ units$','fontname',3); ylabel('$Radians/\pi*exp(0)$','fontname',3,'fontsize',3);
275 xgrid(5,1,7); // color, thickness, style
276 a1=get("current_axes"); // get the handle of the newly created axes
277 //a1.data_bounds=[-4,6,-2,2];
278 // ----------------------------END f7-------------------------------------------
279 //%% END X(w)'s mag ang real imag
280 //%% ---------------------------------------------------------------------------
View Code
三、运行结果
0、窗函数时长都是M=101，区间范围取-π到π。
1、矩形窗
2、汉宁窗
3、三角窗
4、汉明窗
标签：fontname,函数,figure,相位,axes,fontsize,get,DTFT,pi 来源： https://www.cnblogs.com/ky027wh-sx/p/16460158.html