# How to plot frequency spectrum of a signal in matlab?

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Nur Fauzira Saidin
on 26 Oct 2015

Edited: Frantz Bouchereau
on 29 Jul 2021

Hi. I want to plot frequency spectrum of a signal. I got this coding based on the sources that I found from the internet but my lecturer said this is not frequency spectrum. Can somebody help me on this?

close all;

%Define number of samples to take

fs = 8000;

f = 400; %Hz

%Define signal

t = 0:1/fs:1-1/fs;

signal = sin(2*pi*f*t);

%Plot to illustrate that it is a sine wave

plot(t, signal);

title('Time-Domain signal');

%Take fourier transform

fftSignal = fft(signal);

%apply fftshift to put it in the form we are used to (see documentation)

fftSignal = fftshift(fftSignal);

%Next, calculate the frequency axis, which is defined by the sampling rate

f = fs/2*linspace(-1,1,fs);

%Since the signal is complex, we need to plot the magnitude to get it to

%look right, so we use abs (absolute value)

figure;

plot(f, abs(fftSignal));

title('magnitude FFT of sine');

xlabel('Frequency (Hz)');

ylabel('magnitude');

%noise

noise = 2*randn(size(signal));

figure, plot(t,noise), title('Time-Domain Noise');

fftNoise = fft(noise);

fftNoise = fftshift(fftNoise);

figure, plot(f,abs(fftNoise)), title('Magnitude FFT of noise');

xlabel('Frequency (Hz)');

ylabel('magnitude');

%noisy signal

noisySignal = signal + noise;

figure, plot(t,noisySignal), title('Time-Domain Noisy Signal');

fftNoisySignal = fft(noisySignal);

fftNoisySignal = fftshift(fftNoisySignal);

figure, plot(f,abs(fftNoisySignal)), title('Magnitude FFT of noisy signal');

xlabel('Frequency (Hz)');

ylabel('magnitude');

##### 0 Comments

### Accepted Answer

Frantz Bouchereau
on 29 Jul 2021

Edited: Frantz Bouchereau
on 29 Jul 2021

Your code computes FFT and needs some extra normalization steps to calculate true power spectrum.

There are various ways in which you can compute and plot true power spectrum or power spectral density in MATLAB (when I say 'true power spectrum' I mean that the output values correspond to actual power values).

1) If you want to compute the power spectrum without having to specify many parameters and want the function to choose the best parameters for you, you can use pspectrum. Calling the function without outputs will give you a plot with the computed power spectrum.

2) If you want to compute power spectrum or power spectral density and want full control over the window size, window overlap, window type, and number of FFT points, you can use the Welch periodogram pwelch function. Calling the function without outputs will give you a plot with the computed power spectrum.

3) If you want to just visualize the power spectrum, you can use the Signal Analyzer app. The app let's you visualize your signals simultaneously in the time, frequency, and time-frequency domains. You can zoom into signal regions of interest and analyze the spectra at those zoomed regions.

4) If you have split your signals into multiple signal frames you can use the Spectrum Analyzer scope.

Computing true power spectra requires normalization of the FFT and the window used in the computations. Here is a popular MATLAB doc page that explains the relationship between FFT and true power spectra: Power Spectral Density Estimates Using FFT.

##### 0 Comments

### More Answers (3)

Salaheddin Hosseinzadeh
on 26 Oct 2015

Hi there!

I don't know why your instructor didn't like it! Maybe it's missing a division and he is picky on that!

fftNoisySignal = fft(NoisySignal)./numel(NoisySignal);

Maybe that is the case, basically the magnitude of the fft has an issue, I guess! You need to apply this division on every fft command you use.

Hope this helps.

Good luck!

##### 3 Comments

Lazaros Moysis
on 10 Feb 2021

Jonas
on 1 May 2021

Image Analyst
on 26 Oct 2015

Edited: Image Analyst
on 26 Oct 2015

##### 2 Comments

Salaheddin Hosseinzadeh
on 27 Oct 2015

As Image Analyst said there are several different methods. Some of which have different names. Power spectrum, Power spectrum density and ... each of which have slightly different method of calculation. Yet, the simple fft is the heart of them, which is performed correctly in your code.

You already accepted my answer, tnx, but if your problem was not and you're looking for something specific search and if no success let me know :)

Good Luck!

Viktor Bolgov
on 1 Dec 2019

##### 1 Comment

Sandro Yemi Okutuga
on 14 Aug 2020

Edited: Sandro Yemi Okutuga
on 14 Aug 2020

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