How to find RMS bandwidth of the below signal
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L=10;
n=1.45;
c=2.9979e8;
dt=6e-12;
T=10*2*L*n/c;
fmax =2.5e9
%fs=80*fmax;
TA=-T/2:dt:T/2;
fs=1/dt;
%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);
%plot(TA,(EL1t));
%FA = ((0:Nt-1)-floor(Nt/2))/Nt*fs;
FA = (-Nt/2:Nt/2-1)/Nt*fs;
FP=fft(phi);
%fs=1/dt/Nt;
Z=plot(FA,fftshift(abs(fft(EL1t/Nt))));
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1719921/image.png)
1 Commento
dpb
il 22 Giu 2024
Modificato: dpb
il 22 Giu 2024
Let's get a better picture of what the result actually is...
L=10;
n=1.45;
c=2.9979e8;
dt=6e-12;
T=10*2*L*n/c;
fmax =2.5e9;
fmax = 2.5000e+09;
%fs=80*fmax;
TA=-T/2:dt:T/2;
fs=1/dt;
%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);
%plot(TA,(EL1t));
%FA = ((0:Nt-1)-floor(Nt/2))/Nt*fs;
FA = (-Nt/2:Nt/2-1)/Nt*fs;
FP=fft(phi);
%fs=1/dt/Nt;
Z=plot(FA,fftshift(abs(fft(EL1t/Nt))));
set(gca,'YScale','log')
OK, it is all positive; what have you tried so far to simply translate the formula into MATLAB code?
Risposta accettata
Chandrika
il 4 Lug 2024
Hello Yogesh,
From your code, I could understand that 'FA' is the Frequency vector computed using sampling frequency 'fs' and the number of time samples 'Nt'
Further, in order to implement the formula to compute RMS linewidth in your given code, you may refer the sample code I am attaching below:
L=10;
n=1.45;
c=2.9979e8;
dt=6e-12;
T=10*2*L*n/c;
fmax =2.5e9;
fmax = 2.5000e+09;
TA=-T/2:dt:T/2;
fs=1/dt;
Nt=round(T/dt);
vsine = 1;
phi = vsine*sin(2*pi*fmax*TA);
EL1t=1.274e7*exp(1i*phi);
% Frequency vector computed
FA = (-Nt/2:Nt/2-1)/Nt*fs;
% FFT of the signal copmuted and normalized
EL1t_fft = fft(EL1t) / Nt;
% Power computed
Pow = abs(fftshift(EL1t_fft)).^2;
% Computing rms_linewidth as per the formula
rms_linewidth = 2*(sqrt(sum((FA).^2 .* Pow) / sum(Pow)));
Here, 'Pow' indicating the Power has been calculated premised upon the idea that Power is the squared magnitude of a signal's Fourier transform, normalized by the number of frequency samples as could be found in this documentation: https://in.mathworks.com/help/matlab/math/fourier-transforms.html
I hope you find the above provided workaround useful!
Regards,
Chandrika
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