How can I implement these for loops efficiently using covolution?

I have this code

for xx=1:length(x)
    for kk=1:length(x)
        xSinc(xx) = xSinc(xx)+x(kk)*sinc(xx-kk-delta/T);
    end
end

How can implement this efficiently using convultion in MATLAB?

[Torsten]

If you don't know how to spell the method, you'd better stick to your loop solution.

Answer 1

[Dyuman Joshi]

Simple multiplication would be good enough -

xx = 1:length(x);
kk = 1:length(x);

xSinc(xx) = xSinc(xx) + x(kk)*sinc(xx-kk'-delta/T);

[MAWE]

What if kk has other dimension that xx. How can I implement it?

[Dyuman Joshi]

The above code will work for that as well.

[MAWE]

It gives me an error saying matrix dimensions must agree

[Dyuman Joshi]

Please attach your code, so that I can reproduce the error and suggest solutions to tackle the issue.

[MAWE]

OK, it is working. I just needed to transpose one vector. Here another problem I have, the second vector depends on the first as

for xx = 1:length(x)
    for kk=max(xx-L,1):min(xx+L,length(x))
        xSinc(xx) = xSinc(xx)+x(kk)*sinc(xx-kk-delta/T);
    end
end

Currently I am doing this

for xx = 1:length(x)
    kk=max(xx-L,1):min(xx+L,length(x))
    xSinc(xx) = xSinc(xx)+x(kk)*sinc(xx-kk'-delta/T);
end

Is it possible to write this for loop in vector form for efficient implementtaion?

Answer 2

[Bruno Luong]

Use conv

x = (0:0.2:5).^2;
L = 3;
delta = rand; T = rand;

% Your method
xSinc = zeros(size(x));
for xx = 1:length(x)
    for kk=max(xx-L,1):min(xx+L,length(x))
        xSinc(xx) = xSinc(xx)+x(kk)*sinc(xx-kk-delta/T);
    end
end
xSinc

xSinc = 1×26

-0.0051 -0.0070 0.0352 0.1578 0.3593 0.6413 1.0038 1.4468 1.9704 2.5745 3.2591 4.0243 4.8700 5.7962 6.8029 7.8902 9.0580 10.3063 11.6351 13.0445 14.5344 16.1048 17.7558 20.0963 21.1378 24.2622

% conv method
xSinc2 = conv(x, sinc((L:-1:-L)+delta/T), 'same')

xSinc2 = 1×26

-0.0051 -0.0070 0.0352 0.1578 0.3593 0.6413 1.0038 1.4468 1.9704 2.5745 3.2591 4.0243 4.8700 5.7962 6.8029 7.8902 9.0580 10.3063 11.6351 13.0445 14.5344 16.1048 17.7558 20.0963 21.1378 24.2622

norm(xSinc2-xSinc)

ans = 5.7220e-15

plot(xSinc, 'b')
hold on;
plot(xSinc2, 'r.')

[MAWE]

That's an interesting approach, and it's much faster. Thank you!

[MAWE]

Can I ask about the undelying logic you used? Why for exampled you defined

kk = -L:L;

and then fliped the order in

K = flip(sinc(kk+delta/T));

[Bruno Luong]

I can't explain more than it comes from definition of conv adapted to your code.

Have you tried to do some study of the code or you just ask without study conv?