Estimating the power of a signal at different frequencies: aka spectral density estimation

This report has a good write up on using FFTs to make signal amplitude measurements: http://www.schmid-werren.ch/hanspeter/publications/2012fftnoise.pdf

Some example MATLAB code. Three signals are generated at levels of -20 dB, -40 dB & -60 dB:

clear
clf

%sampling frequency
Fs=48000;

%test frequencies
f1=11300;
f2=1510;
f3=17750;

%time
t=(0:1/Fs:1);

%generate signals
% 0.1 amplitude = -20 dB
% 0.01 = -40 dB
% 0.001 = -60 dB
y=0.1*cos(2*pi*f1*t)+0.01*cos(2*pi*f2*t)+0.001*cos(2*pi*f3*t);

%add some random background noise
noise = randn(size(y));
y=y+1e-4*noise;

%wavwrite(y,Fs,'test.wav');

N=1024;
w=blackman(N);

Y=fft(y(1:N).*w');

%scaling factors
%e.g. see
%http://www.schmid-werren.ch/hanspeter/publications/2012fftnoise.pdf
scaling = 2/(mean(w)*N);

fx=Fs/N*(0:N/2-1);
Y=Y(1:N/2);

figure(1)
plot(fx,20*log10(abs(Y) * scaling))

xlabel('Frequency/Hz')
ylabel('Amplitude/dB')
grid