PSD estimation via FFT

Question

I estimate Power Spectral Density (PSD) for Gaussian monopulse in UWB band. I have two codes, using fft. But there is a problem with y axes, since I don't know its dimension (I need PSD in dBm/MHz). And also it should be a mistake in the first code, since it shows only one value at the y axes.

Code1

fs=1e11;

g=0.1e-9;

tmax=1e-9;

fftl=2048;


t=(-tmax:1./fs:tmax)';

s=t./(g.^3.*sqrt(2.*pi)).*exp(-t.^2./(2.*g.^2))./2.5e19;

figure(1)

plot(t,s);

xlabel('Time, s');

ylabel('Amplitude, V');

ffts=abs(fft(s,fftl));

ffts=2.*ffts./fftl;

fftp=abs(ffts.*conj(ffts))./2;

fftps=(fftp-30)./1e-6;

f=0:fs./fftl:fs./2-fs./fftl;

figure(2)

plot(f,fftps(1:length(f))),grid;

xlabel('Frequency, Hz');

Code2

fs=1e11;

g=0.1e-9;

tmax=1e-9;

t=(-tmax:1./fs:tmax)';

s=t./(g.^3.*sqrt(2.*pi)).*exp(-t.^2./(2.*g.^2))./2.5e19;

figure(1)

plot(t,s);

xlabel('Time, s');

ylabel('Amplitude, V');

S=fft(s,8192);

f=fs.*(0:4095)./8192;

Pss=S.*conj(S)./8192;

figure(2)

plot(f,Pss(1:4096));

Thank you so much for any help!

Answer 1

Your second plot should give you a plot with units V^2/Hz.

dBm units are measure of power relative to 1 mW, so you have to know the impedance of your measurement.

So to get to mW/Hz you would want to multiply by 1e6/R, where R is your impedance. Then take 10*log10 of the result and you have dBm/Hz.