Getting different outputs from indexing and graphically.How do I verify this indexing value?..

clear all
close all
clc
L=10;
n=1.45;
Omega=1.020663297455751e+11;
GAMMAb=3.590391604102621e+08;
c=2.9979e8;
dt=6e-12;         %time increment
T=10*2*L*n/c;     %total time
fmax = 1e9;       %maximun frequency
%fs=80*fmax;

TA=-T/2:dt:T/2;   %time axis for the signal
fs=1/dt;          %sampling frequency
%t = (-T/2/dt:1:T/2/dt)*dt;
Nt=round(T/dt);   

vsine = 1;
phi = vsine*sin(2*pi*fmax*TA);
EL1t=1.274e7*exp(1i*phi);   %signal
plot(TA,(EL1t));

Warning: Imaginary parts of complex X and/or Y arguments ignored.

%FA = ((0:Nt-1)-floor(Nt/2))/Nt*fs;
FA = (-Nt/2:Nt/2-1)/Nt*fs;  %frequency axis
FP=fft(phi);                %fft of the signal 
%fs=1/dt/Nt;
figure;
Z=plot(FA,fftshift(abs(fft(EL1t/Nt))));  %fft plot with frequency axis
xlim([(Omega/2/pi-GAMMAb/2/pi/2) (Omega/2/pi+GAMMAb/2/pi/2)])

freqlim1=dsearchn(FA',(Omega/2/pi-GAMMAb/2/pi/2))

freqlim1 = 96299

freqlim2=dsearchn(FA',(Omega/2/pi+GAMMAb/2/pi/2))

freqlim2 = 96355

FA1=freqlim1:freqlim2;
freqlim=dsearchn(FA',Omega/2/pi)

freqlim = 96327

Y1=fftshift(abs(fft(EL1t(freqlim)/Nt)))    %value of the signl at Omega 

Y1 = 79.0205

I have been trying the index of the signal corresponding to frequency at Omega.Graphically it is around 197 and when i substitute the index number in the fft expression , it is showing around 79.

Is this the case of indexing gone wrong??...

Answer 1

[Paul]

L=10;
n=1.45;
Omega=1.020663297455751e+11;
GAMMAb=3.590391604102621e+08;
c=2.9979e8;
dt=6e-12;         %time increment
T=10*2*L*n/c;     %total time
fmax = 1e9;       %maximun frequency
%fs=80*fmax;
TA=-T/2:dt:T/2;   %time axis for the signal
fs=1/dt;          %sampling frequency
%t = (-T/2/dt:1:T/2/dt)*dt;
Nt=round(T/dt);
vsine = 1;
phi = vsine*sin(2*pi*fmax*TA);
EL1t=1.274e7*exp(1i*phi);   %signal
%plot(TA,(EL1t));

%FA = ((0:Nt-1)-floor(Nt/2))/Nt*fs;
FA = (-Nt/2:Nt/2-1)/Nt*fs;  %frequency axis
FP=fft(phi);                %fft of the signal 
%fs=1/dt/Nt;
figure;
Z=plot(FA,fftshift(abs(fft(EL1t/Nt))));  %fft plot with frequency axis
xlim([(Omega/2/pi-GAMMAb/2/pi/2) (Omega/2/pi+GAMMAb/2/pi/2)])

freqlim1=dsearchn(FA',(Omega/2/pi-GAMMAb/2/pi/2))

freqlim1 = 96299

freqlim2=dsearchn(FA',(Omega/2/pi+GAMMAb/2/pi/2))

freqlim2 = 96355

FA1=freqlim1:freqlim2;
freqlim=dsearchn(FA',Omega/2/pi)

freqlim = 96327

At this point, freqlim is a single number

EL1t(freqlim)

ans = 7.1267e+06 + 1.0560e+07i

So its fft

Y1=fftshift(abs(fft(EL1t(freqlim)/Nt)))    %value of the signl at Omega 

Y1 = 79.0205

is simply

abs(EL1t(freqlim))/Nt

ans = 79.0205

Are you trying to find the value of the FFT of EL1t at the frequency closest to Omega? Or something else?

[Yogesh]

I am trying to find the value of fft of El1t at Omega.

That should be equal to the value shown in the plot.

The value in the plot is around 198 and the indexing value is around 79.

This is what I am not understanding.

[Paul]

To find the value of the FFT of EL1t at the frequency closest to Omega, wouldn't that just be (untested)

Y1 = fftshift(abs(fft(EL1t/Nt))));
Y1(dsearchn(FA',Omega/2/pi))

If EL1t is truly finite duration (i.e., not periodic), then you can use freqz to evaluate its Discrete Time Fourier Transform at any frequencies you want (check the doc, you have to query for at least two frequencies).