the FFT is the fast implementation of the DFT
function [Xk] = dft(xn,N)
% Computes Discrete Fourier Transform
% -----------------------------------
% [Xk] = dft(xn,N)
% Xk = DFT coeff. array over 0 <= k <= N-1
% xn = N-point finite-duration sequence
% N = Length of DFT
%
n = [0:1:N-1]; % row vector for n
k = [0:1:N-1]; % row vecor for k
WN = exp(-j*2*pi/N); % Wn factor
nk = n'*k; % creates a N by N matrix of nk values
WNnk = WN .^ nk; % DFT matrix
Xk = xn * WNnk; % row vector for DFT coefficients
function from recommended reading: Digital signal Processing using MATLAB, by V.Ingle J.Proakis
by constraining the key lines to a single frequency, let's say for instance N=N0 the key lines of the DFT get simplified:
WN = exp(-j*2*pi/N0); % it was a vector now just 1x1 complex
now k again is no longer a vector but a 1x1 integer
nk = n'*k;
and the matrix WNnk gets reduced to a linear vector
WNnk = WN .^ nk; % DFT on a single frequency
give me an example and I will calculate the single frequency DFT
Xk = xn * WNnk;
Bear in mind that FFT depends on the lengths of the time vector and the amount of frequency samples you are after, so outcome will vary with varying time sequence lengths, even if same t1 t2 for the input time sequence, if you sample faster or slower the result will vary.
The FFT is a significant improvement in spectrum analysis because it allows to software build many blocks that once had to be hardware, but such variations are one of the factors to correct and make sure do not render useless measurements.
So, rolling back to Start Strider answer: I agree that you'd better know the channel, band you want to work on, and then calculate as many available frequency samples as you can. Then you can take a pick, or interpolate.
if you find my answer useful would you please mark it as Accepted Answer by clicking on the ACCEPT ANSWER button?
thanks in advance for time and attention
John BG
