FFT at specific frequency

Hello,

I'm trying to get a function wich calculate the transform fourrier at specific freqency by using 3 methods, when the first we're using 2 loop,s the second one loop and the last none.

The input of the function are a vector wichs is a sum of cosines, the method choose, a vector time t, delta t and fAxis wich contains the frequency:

clc;clear;close all
delta_t=0.1;
Tlim=5;
f=[1;2];
[t,x]=getSumOfCosines(delta_t,Tlim,f);
[T,tPeriod,xPeriod] = findPeriod(t,x);
fAxis=[6,8,92,12];
method='No Loops';
ft = myFourierTransform(method, t, x, delta_t, fAxis);

function [t,x]=getSumOfCosines(delta_t,Tlim,f)
t=0:delta_t:Tlim;
x=sum(cos(2*pi*t.*f));
end

function [ft] = myFourierTransform(method, t, x, delta_t, fAxis)

if strcmp(method,'2 Loops')
    ft=zeros(length(fAxis),length(t));
    for frequency=1:length(fAxis)
        for time=1:length(t)
            ft(frequency,time)=x(time)*exp(-1i*2*pi*time*fAxis(frequency))*delta_t;       
        end
    end
end
if strcmp(method,'1 Loops')
    ft=ones(length(fAxis),length(t));
    time=1:length(t);
    for frequency=1:length(fAxis)
        ft(frequency,:)=x(time).*exp(-1i*2*pi*time*fAxis(frequency))*delta_t;
    end
end
if strcmp(method,'No Loops')
        ft=ones(length(fAxis),length(t));
        frequency=1:length(fAxis);
        time=1:length(t);
        ind_frequency=1:length(fAxis);
        ft(ind_frequency,:)=x(time).*exp(-1i*2*pi*time.*fAxis(frequency))*delta_t;
    end
end

But I got this error about the no loop method:

Matrix dimensions must agree.

Error in myFourierTransform (line 23)
        ft(ind_frequency,:)=x(time).*exp(-1i*2*pi*time.*fAxis(frequency))*delta_t;

Error in a (line 10)
ft = myFourierTransform(method, t, x, delta_t, fAxis);

Answer 1

[Raunak Gupta]

Hi Ilan,

In the last ‘No Loop’ Method, time and fAxis(frequency) are two different length vectors and you cannot get elementwise multiplication for those. On the Left hand side, ft is a matrix so I see you are trying to get a same size matrix as of ft with this expression exp(-1i*2*pi*time.*fAxis(frequency)). There is a small change you can make that will solve the error.

ft(ind_frequency,:)=x(time).*exp(-1i*2*pi*time.*(fAxis(frequency).'))*delta_t; 

Here I have done transpose of fAxis(frequency) so that multiplication of two vector of size 1 x N and 1 x M will result into a matrix of N x M or M x N based on the order.