# Struggling to decide the sampling frequency for this fft plot

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Yogesh on 24 Apr 2024
Commented: Yogesh on 24 Apr 2024
clear all
close all
clc
L=10;
n=1.45;
Can you guys help me with assigning the frequency values along the x axis , I am bit confused on how to determine the sampling frequency for a fft
c=2.9979e8;
dt = 6e-12;
T=10*2*L*n/c;
t = (-T/2/dt:1:T/2/dt)*dt;
Nt=round(T/dt);
fsine = 1e9;
vsine = 1;
phi = vsine*sin(2*pi*fsine*t);
EL1t=1.274e7*exp(1i*phi);
FP=fft(phi);
fs=(-Nt/2:1:Nt/2-1);
Z=plot(fs,fftshift(abs(fft(EL1t))));

David Goodmanson on 24 Apr 2024
Edited: David Goodmanson on 24 Apr 2024
Hi Yogesh,
If the time array has spacing delt (which you denote by dt) and the frequency array has spacing delf, then for an N-point fft the relationship between the two quantities is always
delt*delf = 1/N (1)
.That's because the total length of the time record is T = N*delt, and (not counting DC) the periodic function with the smallest possible frequency delf has one oscillation in that time, so delf = 1/T. The higher frequencies have n oscillations in time T and are integer multplies of delf, f = delf*n which produces the frequency grid and justifies identifying 1/T as delf. Then (1) follows.
Yogesh on 24 Apr 2024
Hey thanks David , you are a life saver...