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% Multimedia Signal Synthesis at CTU Prague 
% Copyright © 2015 by Roman Cmejla
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% Suggestions for 5th laboratory: 
% Subtractive synthesis
% October 30, 2015
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% Example 1:  Differentiator and integrator - simulation
% Generate a short numerical sequence and verify the behavior of differentiator 
% and integrator for differential equations that describe these filters
% a) using function for,
% b) using function diff and cumsum,
% c) using function filter

% Solution
x=[0 0 0 0 5 5 5 5 8 8 8 8 3 3 3 3 5 5 5 5];
y_int(1)=x(1);
for n=2:length(x)
           y_dif(n)=x(n)-x(n-1); 
           y_int(n)=x(n)+y_int(n-1);
end;
subplot(231), 
plot(y_dif), hold on, plot(x,':r'), hold off
legend('cyklus for'), xlabel('---> n')
subplot(234), plot(y_int), hold on, plot(x,':r'), hold off
legend('cyklus for'), xlabel('---> n')

subplot(232), plot([0 diff(x)]), 
hold on, plot(x,':r'), hold off
legend('diff'), xlabel('---> n')
subplot(235), plot(cumsum(x)), 
hold on, plot(x,':r'), hold off
legend('cumsum'), xlabel('---> n')

subplot(233), plot(filter([1 -1],1,x)), 
hold on, plot(x,':r'), hold off
legend('filter'), xlabel('---> n')
subplot(236), plot(filter(1,[1 -1],x)), 
hold on, plot(x,':r'), hold off
legend('filter'), xlabel('---> n')

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% Example 2:  Differentiator and integrator - behavior
% Generate multiple periods of digital sinusoidal, rectangular 
% and sawtooth waveform.
% a) Display the output signal of differentiator
% b) Display the output signal of integrator

x1=sin(0:0.2:10-0.2);
x2=square(0:0.2:10-0.2);
x3=sawtooth(0:0.2:10-0.2,.5);

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% Example 3:  Speech filtering
% a) Listen the speech signal at the output of the lowpass filter
% b) Listen the speech signal at the output of the highpass filter
% c) Compare the sum of the filtered signals with the original
% d) Analyze the used filters 
%    (frequency response, impulse response, the distribution of zeros and poles)

b_dp=[1  1];  a_dp=[1 -0.9]; % LP
b_hp=[1  -1]; a_hp=[1 0.9];  % HP
jedna=wavread('jedna.wav');

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% Example 4:  Speech filtering using digital filter with one pole
% Repeat the task of the previous example for a simple digital filter 
% whose pole has a radius of: 
% a) r = 0,9
% b) r = 0,95
% c) r = 0,99
% d) r = -0,9
% e) r = -0,95
% f) r = -0,99

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% Example 5:  Envelope detector
% Realize envelope detectors

load osum1.sig
xc=osum1./max(abs(osum1)); plot(xc,'k') 

xi=filter(1,[1 -0.99],abs(xc)); plot(xi,'k'), 
xi=filter(1,[1 -0.8],abs(xc));  plot(xi,'k'), 
xi=filter(1,[1 -0.3],abs(xc));  plot(xi,'k'), 

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% Example 6:  Peak detector
%load osum1.sig

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% Example 7:  Applications with noise and envelopes
% efekty

fs=44100;
doba=2.5;
t=0:1/fs:doba-1/fs;
x=randn(1,doba*fs);
X=[0 0.05 0.4  1];
Y=[1 0.05 0.25 0];
O=interp1(X,Y,t./t(end));
sig=x.*O;
soundsc(sig,fs)

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% Example 8:  Tuning filter               
% Continuously  (according to the sine wave) tune 
% the 1st order IIR filter (by changing the coefficient) 

% Put the white noise on the input of the filter 

fs   =  8000;                % sampling frequency [Hz]
fm   =  .5;                  % frequency of control sinusoidal signal
doba =  6;                   % duration of output signal [s]
nT   =  0:1/fs:doba-1/fs;    % time axis
x=rand(1,length(nT))-.5;

% Display:
% - control signal
% - output signal
% - spectrogram of output signal

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% Example 9: Applications with noise and envelopes 
% 
% Realize a simple drum on the principle of filter synthesis
% Filter parameters: b=1; a=[1 -0.7934];

x=2*rand(1,fs*doba)-1;  % white noise generator

fs   =  44100;          % sampling frequency [Hz]
doba =  .5;             % duration of output signal [s]
nT=0:1/fs:doba-1/fs;    % time axis

% control points of the output signal envelope 
X  =[0 .15 1];          % tame axis
Y  =[1 .05 0];          % amplitude

% Display: 
% - Poles and zeros 
% - Amplitude frequency characteristics 
% - Amplitude envelope 
% - Output waveforms

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% Example 10:  Applications with noise and envelopes
% falling tones

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% Example 11:  Applications with noise and envelopes
% steam engine