# How to understand spectrogram function

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Mark Golberg on 31 Jan 2016
Commented: Aditya Ramesh on 1 Dec 2021
Hello, can someone explain please (in plain english as much as possible) what's the difference between:
1) [s,w,t] = spectrogram(x,window,noverlap,w) returns the spectrogram at the normalized frequencies specified in w.
and
2) [s,f,t] = spectrogram(x,window,noverlap,f,fs) returns the spectrogram at the cyclical frequencies specified in f.
maybe someone can provide a simple example.
THANK YOU

Vidya Viswanathan on 4 Feb 2016
The primary difference between the two is in the way the input signal is specified. In the first statement, the signal 'x' is expected to be specified in terms of normalized frequency while the latter uses the actual frequency of the signal in Hz and the sampling frequency. To understand the difference better, consider the following code snippet:
n = 0:999;
x1 = cos(pi/4*n)+0.5*sin(pi/2*n);
fs = 1000;
t = 0:0.001:1-0.001;
x2 = cos(2*pi*125*t)+0.5*sin(2*pi*250*t);
freq = [125 250];
In the above case, both the signals x1 and x2 are basically the same signal but expressed using the two different representations (x1 uses normalized frequency and x2 uses the cyclical frequency).
The spectrogram for the two signals can be visualized using:
[s1,w,t1]=spectrogram(x1,[],8,[pi/4 pi/2]);
figure,
spectrogram(x1,'yaxis')
[s2,f,t2]=spectrogram(x2,[],8,freq,fs);
figure,
spectrogram(x2,[],[],[],fs,'yaxis')
You can notice that the two spectrograms are similar except for a difference in the magnitudes of the power because they are represented in different units. In the first case, the units is dB/rad/sample while the second representation uses dB/Hz.
Computing the power spectral density of the two signals will give you a better insight about the difference. Consider the following lines of code:
[pxx1,w] = periodogram(x1,[],[pi/4 pi/2]);
pxx2 = periodogram(x2,[],freq,fs)
The magnitudes of pxx1 and pxx2 are different only due to the difference in the units. The conversion from one to another follows the relation:
PSD (in normalized frequency)= (PSD (in cyclical frequency) * Sampling frequency) /(2*pi).
##### 2 CommentsShowHide 1 older comment
Mohannad suleiman on 27 Feb 2021
dear vidya how can we show the (power / frequency ) in the figures

Jonathan Grimbert on 23 May 2018
thanks Vidya Viswanathan for your answer. However I got a question on the X axis... How do you know it is in ms for the second spectrogram ?

Zulfidin Khodzhaev on 18 Dec 2018
Is it possible to get rid of "colorbar", which is automatically there with "spectrogram" command ?
Pawan Sharma on 12 Feb 2019
%% use this to get rid of the colorbar at the end of your plot syntax
colorbar off

Mohannad suleiman on 27 Feb 2021
dear vidya how can we show the (power / frequency ) in the figures
Aditya Ramesh on 1 Dec 2021
colorbar off
This disables the colorbar
colorbar on
This shows the colorbar without the bar label (power/frequency)
Colorbar with the legend label is shown by default even if no colorbar properties are defined. SO basically write nothign after spectrogram(.......) to get what you want.

Christoph on 25 Aug 2021
You can also have a look here --> https://github.com/Christoph-Lauer/Sonogram