why my deconvolution want fit my analytique form?

Question

Rabih Sokhen 2022-2-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1643370-why-my-deconvolution-want-fit-my-analytique-form

评论： Rabih Sokhen 2022-2-7

hy guys,

i am trying to deconvolute a signal to refind my 2 initial signals, however when a = sinc(f) my deconvolution want fit the analytic but if i replace my sinc with sin it fit very well, any idea about this or did i miss something in the code?

thank you in advance

code:

clear all

clc

dt=0.1;

t=-10:dt:10;

z=numel(t);

df = 1/dt;

f = linspace(-df/2, df/2, z);

ff = linspace(-df/2, df/2, z/2);

to=1;

a=to*sinc(to*f);

b=1./(1+1i*2*pi*f);

y_f=conv(a,b);

[bb,r]=deconv(real(y_f),a); %bb should be similar to b

[aa,r]=deconv((y_f),real(b)); %aa should be similar to a

subplot(131)

plot(real(y_f),'r')

title('y_f= \tau*sinc(\tau*f) * 1./(1+1i*2*pi*f)')

subplot(132)

plot(f,real(aa),'r')

hold on

plot(f,a,'*k')

subplot(133)

plot(f,real(bb),'r')

hold on

plot(f,real(b),'*k')

ylim([0 2])

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Answer 1

Paul 2022-2-4

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https://ww2.mathworks.cn/matlabcentral/answers/1643370-why-my-deconvolution-want-fit-my-analytique-form#answer_889185

在 MATLAB Online 中打开

For a real and b complex, the theoretical equations should be (illusrated with short sequences)

a = rand(1,5);
b = rand(1,5) + 1j*rand(1,5);
y_f = conv(a,b);
aa = deconv(real(y_f),real(b)); % or aa = deconv(imag(yf),imag(b))
bbreal = deconv(real(y_f),a);
bbimag = deconv(imag(y_f),a);
% check
a - aa
ans = 1×5
	1.0e+-15 *

         0   -0.1110    0.2776         0   -0.3331
real(b) - bbreal
ans = 1×5
	1.0e+-15 *

         0   -0.0555    0.0555   -0.2220         0
imag(b) - bbimag
ans = 1×5
	1.0e+-15 *

         0         0         0   -0.1110    0.2220

As we can see,, even for these "simple" sequences deconv is not exact (which I gues is not surprising). Trying these equaations on the a and b in the Question resulted in a good reconstruction of a, but not of b, which blew up very quickly. Maye deconv is very numerically sensitive operation, at least for the given inputs.