Multiply vector elements by their index (optimization question)

I'm looking to multiply elements of a vector by their respective index. Right now, I'm using the following code (variable names simplified and shortened):

for a = 0:Points-1  
 for b = 0:Points-1
  ary1( a+1 ) = ary1( a+1 ) + ary2( b+1 ) * exp( i*a*b/Points );

I'd like to be able to change this into a vector operation in either direction, such as

for a = 0:Points-1  
 ary1( a+1 ) = ary1( a+1 ) + ary2 .* exp( i*a*b/Points );

The problem, of course, is that b no longer exists, nor can I make something that is a function of a that returns the appropriate b.

If it's relevant, the specific purpose of this code is DFT implementation. I do realize that MATLAB provides FFT as a built-in function, however, I need specific control that I can't get with the FFT functions provided with MATLAB.

Hopefully my question makes sense. Thank you for your time.

Answer 1

[Sean de Wolski]

%Sample data
ary1 = (1:10).';
ary2 = rand(1,10);
Points = 10;

%Matrix Method
v = (0:(Points-1));
ary4 = ary1+sum(exp(1i*(v'*v)/Points)*ary2',2);

%Your method
for a = 0:Points-1  
 for b = 0:Points-1
  ary1( a+1 ) = ary1( a+1 ) + ary2( b+1 ) * exp( 1i*a*b/Points );
 end 
end

%Check!
isclose = @(x,y)isequal(size(x),size(y))&&all(abs(x(:)-y(:))<10^-10);
isclose(ary1,ary4)

[Scott]

Thanks for the quick reply.

There are two things, at least. The first is that it requires the same amount of points in both time and frequency domain representations of a signal.

The second is that is it requires a spectrum to start at 0, and when working with signals that have high frequency, this can make inconveniently large vectors.

[Scott]

Yes, it did.