Vectorize application of xcorr() function

For the following code,

t = 0:1e-3:1-1e-3;

AF_hat = [];

fd_ = -8:0.1:8;

for fd = fd_

AF_hat = [AF_hat; xcorr(s,s.*exp(-1i*2*pi*fd*t))*Ts];

end

I would like to eliminate the for loop by doing something like,

xcorr(s,s.*exp(-1i*2*pi*fd_.'*t))*Ts,

but cannot get it to work.

Would welcome any comments/guidance.

Answer 1

[Bruno Luong]

Vectorized method but for-loop with preallocation is faster

t = 0:1e-3:1-1e-3;
Ts = 5e-2; 
fd_ = -8:0.1:8;
s = rand(size(t));
tic
AF_hat = zeros(length(fd_),2*length(s)-1);
for k = 1:length(fd_)
    fd = fd_(k);
    AF_hat(k,:) = xcorr(s,s.*exp(-1i*2*pi*fd*t))*Ts;
end
toc

Elapsed time is 0.074924 seconds.

% vectorize way
tic
A_hat2 = conv2(s,flip(conj(s.*exp(-1i*2*pi*fd_(:).*t))*Ts,2));
toc

Elapsed time is 0.083580 seconds.

% Check correctness
norm(AF_hat-A_hat2,Inf)/norm(AF_hat,Inf)

ans = 6.7209e-16

[Bruno Luong]

May be faster code since avoid conj and replace flip array by 2 vector-flips

t = 0:1e-3:1-1e-3;
Ts = 5e-2; 
fd_ = -8:0.1:8;
s = rand(size(t));

% vectorize way
tic
A_hat2 = conv2(s,(Ts*flip(s)).*exp(2i*pi*fd_(:).*flip(t)));
toc

Elapsed time is 0.076804 seconds.