The sampling frequency is the inverse of the sampling interval. The sampling frequency appears to be ‘ts’ .
These correspond to the MATLAB fft documentation for the frequency vector:
Fv = linspace(-Fs/2, Fs/2-Fs/length(s), length(s)); % EVEN 'length(s)' (Asymmetric)
Fv = linspace(-Fs/2, Fs/2, length(s)); % ODD 'length(s)' (Symmetric)
where ‘s’ is the signal vector (or by default, the columns of a signal matrix).
% Sampling Time
ts = 1000;
% Time domain variables
t1=-2:1/ts:2;
t2=2:1/ts:4;
% Evaluation at those time domains
x1=4*ones(size(t1));
x2=-8*ones(size(t2));
% Combining both time domains of the piecewise functions
t=[t1 t2];
% Combining functions
f=[x1 x2];
% Plot the piecewise function with respect to time
figure(1);
plot(t,f);
ylim([-10 6]);
% Unsure of this part's sample and frequency domain
% I chose the sample based on the size of the combined time (t).
% Samples
N=6002;
% Frequency Domain (
freq=-ts/2:ts/(N-1):ts/2
Fv = linspace(-ts/2, ts/2-ts/length(f), length(f)) % EVEN 'length(s)' (Asymmetric)
% Fourier transform of the piecewise function (f)
% % ft=fft(fftshift(f));
ft = fftshift(fft(f));
Size_ft = size(ft)
% Figure 2 shows the absolute of the fourier transform with respect to the
% frequency
figure(2);
plot(freq,abs(ft));
grid
grid('minor')
The only change I made to your code was to change the order of the fft and fftshift calls, since that is apparently what you intend.
Your ‘freq’ and my ‘Fv’ are slightly different because they are calculated differently, however they are essentially the same. (I did that to check. Use yours.)
.
