# how to get real frequency components using MUSIC compute frequency?

7 views (last 30 days)
evelyn on 26 Nov 2023
Commented: Chunru on 30 Nov 2023
I used pmusic ( https://au.mathworks.com/help/signal/ref/pmusic.html ). It seems that pmusic cannot get real frequency for the signal.
x = cos(0.257*pi*n) + sin(0.2*pi*n) + 0.01*randn(size(n))
should have frequency components of 0.1258 and 0.1.
1. pmusic with No Sampling Specified example
But, the peaks for x-axis(normalized frequency) are 0.257 and 0.2.
2. Specifying Sampling Frequency and Subspace Dimensions example
But, the peaks for x-axis( frequency) are 812(=0.2*fs/2) and 1258(=0.257*fs/2) .
It seems that pmusic cannot get real frequency for the signal? So the peaks at x-axis is not the real frequency? what is the actually frequency? how could I get them for pmusic
Walter Roberson on 26 Nov 2023
When you pass fs of 8000 into the first pmusic() call, you are lying completely about the sampling frequency.
evelyn on 26 Nov 2023
how should I set the fs for the first pmusic call?
x = cos(0.257*pi*n) + sin(0.2*pi*n) + 0.01*randn(size(n)) have frequency components of 0.1258 and 0.1.
when I set fs= 2*0.1258=0.257, the result of frequency still seems not right?
rng default
n = 0:199;
x = cos(0.257*pi*n) + sin(0.2*pi*n) + 0.01*randn(size(n));
[P,f] = pmusic(x,[Inf,1.1],[],0.257,7); % Window length = 7
plot(f,20*log10(abs(P)))
xlabel 'Frequency (Hz)', ylabel 'Power (dB)'
title 'Pseudospectrum Estimate via MUSIC', grid on

Chunru on 27 Nov 2023
rng default
n = 0:199;
f1 = 0.257/2; f2 = 0.2/2;
fs= 2; % fs (fs>2*max(f1, f2)
% generate signal according to f1, f2, fs
t = n/fs;
x = cos(f1*2*pi*t) + sin(f2*2*pi*t) + 0.01*randn(size(t));
nfft=1024;
[P,f] = pmusic(x,4,nfft,fs,7); % Window length = 7
plot(f,20*log10(abs(P)))
xlabel 'Frequency (Hz)', ylabel 'Power (dB)'
title 'Pseudospectrum Estimate via MUSIC', grid on
xline([f1 f2])
evelyn on 30 Nov 2023
how to choose a proper fs and window length?
when I set fs to 0.4, what is the proper window length?
Chunru on 30 Nov 2023
Fs should be at least 2x of the max freq of interest to satisfy the sampling requirement.
Window length should be long enough to resolve the frequencies. For conventional method using FT to estimate spectrum, L is proportial to fs/delta_f. For the example above:
f1 = 0.257/2; f2 = 0.2/2;
fs= 3;
% Length of windows for conventional FT
fs/abs(f2-f1)
ans = 105.2632
For MUSIC, the windown length can be significantly smaller. The exact number is subject to SNR, noise properties, signal properties and so on (since signal and noise subspaces are estimated from the data).

### Categories

Find more on Subspace Methods in Help Center and File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!