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1 I: MATLAB 2005 MATLAB 1. MATLAB 2. MATLAB 3. MATLAB kitahara/local/matlab/ 1 MATLAB 1.1 MATLAB MATLAB 1 FFT 1.2 MATLAB MATLAB PC Windows URL MATLAB Windows kitahara@kuis.kyoto-u.ac.jp 1

2 MATLAB UNIX %matlab MATLAB %matlab -nodesktop MATLAB MATLAB MATLAB >> quit 2

3 2 MATLAB 2.1 MATLAB >> ans = 8 >> 5-3 ans = 2 >> 5 * 3 ans = 15 >> 5 / 3 ans = >> 5 \ 3 ans = 0.6 >> 5 ^ 3 ans = 125 >> mod(5, 3) ans = 2 3

4 >> 1-3 * i ans = i >> a = 3; >> b = 2; >> a + b ans = 5 MATLAB MATLAB MATLAB whos >> whos Name Size Bytes Class a 1x1 8 double array b 1x1 8 double array ans 1x1 8 double array 4

5 >> x = [1 2 3] x = >> x = [1, 2, 3] x = >> x = [1; 2; 3] x = >> x = [1 2 3] x =

6 >> x = 1 : 10 x = >> x = (1 : 10) x = >> x = 1 : 2 : 10 x = >> x = (1 : 5) * 2 x =

7 >> A = [1 2 3; 4 5 6] A = >> A = [1 2 3; 4 5 6] A = >> A = [1 2; 3 4]; >> B = [5 6; 7 8]; >> A + B ans = >> A * B ans = >> A.* B ans = MATLAB * / \ ^.*./.\.^.+.- 7

8 1 { x +4y =1 2x +3y = 1 ( )( x y ) ( = 1 1 ) ( x y ) ( = ) 1 ( 1 1 ) >> [1 4; 2 3] \ [1; -1] ans = MATLAB zeros(m, n) 0 m n ones(m, n) 1 m n repmat(a, m, n) A m n find(a) A find(x>100) sum(a) A mean(a) A std(a) A 8

9 m MATLAB m ave.m function x = ave(a, b, c) x = (a + b + c) / 3; >> ave(6, 7, 8) ans = 7 if for while if a > 0 command1; elseif a == 0 command2; else command3; end for i = 1 : 10 x = x + i * i; fprintf(1, %d\n, x); end while result > 0 result = command(a, b, c); end & ~ any all 9

10 2.2 >> x = 0 : pi / 100 : 2 * pi; >> y = sin(x); >> plot(x, y); 2 >> x = 0 : pi / 10 : 2 * pi; >> y = sin(x); >> plot(x, y, o ); >> figure(2) 2 ID >> hold on >> figure 1 >> x = 0 : pi / 100 : 2 * pi; >> y = sin(x); >> plot(x, y); >> hold on >> x = 0 : pi / 10 : 2 * pi; >> y = sin(x); >> plot(x, y); >> hold off 10

11 2.3 MATLAB MATLAB for for 2 function S = test1(n) S = 0; for i = 1 : n S = S + i * i; end function S = test2(n) a = 1 : n; S = sum(a.* a); tic toc >> tic; test1(1000), toc >> tic; test2(1000), toc 2 for i = 1 : m for j = 1 : n A(i, j) = i * j; end end 11

12 2.4 MATLAB MATLAB char 1 n >> S = hello ; >> whos Name Size Bytes Class S 1x5 10 char array fprintf(id, S) ID id S id 1 C ischar(s) S isempty(s) S 0 0 strcmp(s 1, S 2 ) 2 S 1,S 2 strfind(s, p) S p num2str(x) x int2str(x) x str2num(x) x >> S1 = Hello ; >> S2 = World ; >> S = [S1 S2] S = HelloWorld >> S = [S1 S2] S = Hello World 12

13 fopen 1 fgetl fgets 2 mytype.m function mytype(filename) fid = fopen(filename, r ); while 1 line = fgetl(fid); if ~ischar(line) break; end fprintf(1, [line \n ]); end 3 strtok >> S = I have a pen ; >> [token, rest] = strtok(s) token = I rest = have a pen >> [token, rest2] = strtok(rest) token = have rest = a pen 13

14 3 (x, y, z) readxyz.m function [x, y, z] = readxyz(filename) fid = fopen(filename, r ); i = 1; while 1 line = fgetl(fid); if ~ischar(line) break; end [token, line] = strtok(line); x(i) = str2num(token); [token, line] = strtok(line); y(i) = str2num(token); [token, line] = strtok(line); z(i) = str2num(token); i = i + 1; end

15 2.5 GUI MATLAB GUI GUI GUI figure >> figure( Name, GUITest, Position, [ ],... Tag, GUITest, Risize, off ); figure figure(propertyname1, PropertyValue1, PropertyName2, PropertyName2,...) q Name Position [int int int int] x y Tag GUI Resize on / off GUI GUI uicontrol figure uicontrol(propertyname1, PropertyValue1, PropertyName2, PropertyName2,...) Style GUI pushbutton, togglebutton, radiobutton, checkbox, edit, text, slider, frame, listbox, popupmenu Position [int int int int] figure Tag figure String Value GUI GUI Callback MATLAB FontName FontSize MATLAB 15

16 4 1 GUI GUITest.m function GUITest fig = figure( Name, GUITest, Position, [ ],... Tag, GUITest, Resize, off ); slider = uicontrol( Style, slider, Position, [ ],... Tag, slider1, Callback, update ); edt = uicontrol( Style, edit, Position, [ ],... Tag, edt1 ); update.m update update 7 GUI GUI GUI Callback 1 Callback 2 Callback update update update.m function update % GUI GUI 3 findobj objhandle = findobj( Tag, TagValue) Tag TagValue GUI objhandle MATLAB set get 16

17 set set(objhandle, PropertyName, PropertyValue) objhandle GUI get x = get(objhandle, PropertyName) objhandle GUI 5 2 GUI update.m function update slider = findobj( Tag, slider1 ); edt = findobj( Tag, edt1 ); newvalue = get(slider, Value ); set(edt1, String, num2str(newvalue)); 8 3 GUI 2.6 >> help fft FFT Discrete Fourier transform. FFT(X) is the discrete Fourier transform (DFT) of vector X. For matrices, the FFT operation is applied to each column. For N-D arrays, the FFT operation operates on the first non-singleton dimension.... >> helpdesk 17

18 3 3.1 f A y = A sin(2πft) Hz >> t = 0 : 1/44100 : 5; >> y = 0.9 * sin(2 * pi * 440 * t); >> wavwrite(y, 44100, 16, test1.wav ); 9 262Hz Hz 2 3 >> t = 0 : 1/44100 : 5; >> y = 0.4 * sin(2 * pi * 440 * t) * sin(2 * pi * 880 * t) * sin(2 * pi * 1320 * t); >> wavwrite(y, 44100, 16, test2.wav ); GUI [ ] [ ] 12 18

19 FM FM y = A sin(2πf C t + I sin(2πf M t)). A f C, f M I sin sin sin FM 8 FM >> t = 0 : 1/44100 : 5; >> y = 0.9 * sin(2 * pi * 220 * t + sin(2 * pi * 880 * t)); >> wavwrite(y, 44100, 16, test3.wav ); 13 ( white noise) MATLAB randn >> fs = 44100; >> y = randn(1 * fs, 1); >> wavplay(y, fs); 14 19

20 >> t = 0 : 1/44100 : 2; >> A1 = linspace(0, 0.99, 0.02 / 44100); >> A2 = linspace(0.99, 0, length(t) / 44100); >> A = [A1 A2]; >> y = A.* sin(2 * pi * 440 * t); >> wavwrite(y, 44100, 16, test4.wav ); f * t f.* t 15 >> t = 0 : 1/44100 : 1; >> f = linspace(440, 880, length(t)); >> y = 0.9 * sin(2 * pi * f.* t); f * t f.* t amplitude modulation, AM frequency modulation, FM 1 20

21 3.2 MATLAB GUI GUI GUI AM FM 2 GUI Hz 660Hz 880Hz 220Hz 220Hz 11 21

22 ms /100 cent f[hz] f[cent] = 1200 log / sound1.txt sound1.txt

23 31 2 sound2.txt sound3.txt

24 3.3 (Fourier transform) f(t) f(t) F (ω) f(t) = 1 F (ω)e iωt dω 2π F (ω) F (ω) = f(t)exp(jωt)dt j (discrete Fourier transform; DFT) y(n) Y (e jω )= n y(n)exp( jωn) 2 (fast Fourier transform; FFT) 2 2 MATLAB 2 10 >> t = 0 : 1/44100 : 5; % >> y = 0.9 * sin(2 * pi * 440 * t); % 440Hz >> Y = fft(y); % >> f = linspace(0, 44100, length(y)); % >> plot(f, abs(y)); % 3 0 f s Hz f s 4 0 f s /2Hz 2 t n 3 abs 4 fhz 2fHz f shz f s/2hz 24

25 >> t = 0 : 1/44100 : 5; % >> y = 0.9 * sin(2 * pi * 440 * t); % 440Hz >> Y = fft(y); % >> Y = Y(1 : length(y) / 2 + 1); % >> f = linspace(0, 22050, length(y)); % >> plot(f, abs(y)); % (short-time Fourier transform, short-term Fourier transform; STFT) >> [y, fs, bits] = wavread( sample1.wav ); % sample1.wav >> y1 = y(1 * fs + (0 : 4095)); % >> Y1 = fft(y1); % >> Y1 = Y1(1 : length(y1) / 2 + 1); % >> f = linspace(0, fs/2, length(y)); % >> plot(f, abs(y)); % N { 1 (if 0 n N 1) w(n) = 0 (if n N) (rectangular window) N ( ) 2πn cos (if 0 n N 1) (Hanning window) w(n) = N 1 0 (if n N) ( ) 2 pin cos (if 0 n N 1) (Hamming window) w(n) = N 1 0 (if n N) (window function) 25

26 MATLAB hanning(n) hamming(n) >> [y, fs, bits] = wavread( sample1.wav ); % sample1.wav >> y1 = y(1 * fs + (0 : 4095)); % >> w = hanning(y1); % >> y1 = w.* y1; % >> Y1 = fft(y1); % >> Y1 = Y1(1 : length(y1) / 2 + 1); % >> f = linspace(0, fs/2, length(y)); % >> plot(f, abs(y)); % (spectrogram) MATLAB specgram specgram(y, N, f s, w, N overlap ) y N f s w N overlap >> [y, fs, bits] = wavread( sample1.wav ); % sample1.wav >> specgram(y, 4096, fs, hanning(4096), * fs); % 32 wav 33 specgram fft for specgram [Y, F] = specgram(y, N, f s, w, N overlap ) >> [y, fs, bits] = wavread( sample1.wav ); % sample1.wav >> [Y, F] = specgram(y, 4096, fs, hanning(4096), * fs); % >> plot(f, Y(:, 100)); % 1 26

27 3.4 2 function F0 = estimatef0(filename, th) [y, fs, bits] = wavread(filename); % sample1.wav [Y, F] = specgram(y, 4096, fs, hanning(4096), * fs); % Y = abs(y); Y(max(max(Y))./ Y > th) = 0; % for n = 1 : size(y, 2) Y1 = Y(:, n); dy1 = diff(y1); d2y1 = diff(dy1); s = sign(dy1(1 : end-1)).* sign(dy1(2 : end)); i = find(s == -1); i = i(d2y1(i) < 0); F0(n) = min(f(i)); end % n % % 2 % % % 2 pick up % 440Hz 440Hz 2 880Hz Hz 34 MATLAB y(t) τ y(t + τ) τ τ 35 MATLAB 27

28 y(t) g(t) v(t) Y (ω) Y (ω) = G(ω) V (ω). log Y (ω) = log G(ω) + log V (ω). k log Y k =log G k +log V k C n = 1 ( log G k exp j 2πkn ) + 1 N N N k ( log V k exp j 2πkn ) N (cepstrum coefficient) (quefrency) 36 MATLAB 37 MATLAB

29 L A TEX Word

30 5 MATLAB [1] Get Started with MATLAB, MATLAB [2] MATLAB [3] MATLAB [4] MATLAB CG [5] [6] CQ [7] MATLAB [8] MATLAB [9] H MATLAB DSP [10] Vol.56, No.2, pp ,

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