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

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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

##### 4 Comments

Walter Roberson
on 26 Nov 2023

### Answers (1)

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])

##### 4 Comments

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)

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).

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