Visualising fft-signal__Waterplot - matlab

Question

This is the kind of plot i imagined myself.
https://de.mathworks.com/help/matlab/ref/waterfall.html
Ok, i don't want to explain too much, how my code works. It would take too much time. Just try the second code yourself. Take any small wav-file you can find. When you compile the code, you can see three frequency bands and see that many spectrums are plotted every 30ms. If you have a specifically question concerning my code, how it works, ask me in the comments.
I want every spectrum, at least from one frequency band, to plot it in a 3-dimensional plot. In short, what are the coordinates of the first spectrum and the 2nd, the 3rd, the 4th and so on.
My time segment on which is a fft applied, is 30 ms long. The first point on the x-axis is 30 ms, the next one 60ms and the next one 90ms and so on. What is the y-coordinate from the 30ms? This would be on the frequency axis or the y-axis. The z-axis would be the magnitude out of a frequency component at some point in time (or at a given sliding window frame). How can i do that? How do i write that? I am having big trouble with this matter. And since every explanation is in another language, it makes it much more harder for me.
As you may know, i have an audiofile (music) on which i compute a STFT. I want to visualise it. See the following explanation in my code. Read the comments!
My first idea to do this way, was using the function "mesh" or something similar.
Here is my mesh-code:
X=1:10;
Y=1:15;
Z = [];
% Here i would define the number of time segments
% See the next following code, to understand, what i mean.
for i = 1:length(X)
% Here in this line, i want to compute my short fft
%
% number of frequencies
for j = 1: length(Y)
Z(j,i) = 1.0/(i*j);
end
end
mesh(X,Y,Z)
This code plots me a mesh, i just wanted to know for myself, how this works. Anyway please be aware, that i am quite sure that i do not know, how the function "mesh" works to the fullest, but i think, i understood most of it.
Another thing i need to mention is, that i am defining frequency bands in my next following code. I did this, because i noticed, i have very high amplitudes in a range from 1 - 1000Hz, which is why, i defined 3 frequency bands. It is not necessary to plot all of them, but i want to visualise at least one. Not visualising the whole frequency range from the audio signal, but only the specificially chosen band.
%% MATLAB
%_________________________________________
[y,fs]=audioread('dontstopmenow.wav');
% audioread = Read WAV-file
% y = Vector, which contains audio signal
% fs = Sample Rate
% 'dontstopmenow' = WAV-file
%_________________________________________
%PARAMETER FOR STFT
%_________________________________________
t_seg=0.03; % Length of segment in ms
fftlen = 4096; %FFT-Points
%Defining the length of my frequency bands
f_LOW= 1:200; % contain lower frequencies
f_MEDIUM= 201:600; % contain medium frequencies
f_HIGH= 601:1000; % contain higher frequencies
%_______________________________________________________
segl =floor(t_seg*fs);
% Length of segment, on which we use the fft
% "floor" rounds off the result
windowshift=segl/2;
% size of window which goes to the next segment
window=hann(segl);
%hann function
window=window.';
% From a row vector to a column vector
si=1;
%Start index
ei=segl;
%End index
N= length(y)/windowshift - 1;
% Number of time segements in audio signal
f1=figure;
% New window
f=0:1:fftlen-1;
f=f/(fftlen-1)*fs;
% frequency vector
Ya=zeros(1,fftlen);
%Plotting time segments!
for m= 1:1:N
y_a = y(si:ei);
y_a= y_a.*window;
Ya=fft(y_a, fftlen);
Ya=abs(Ya(1:end/2));
%One-sided-spectrum
drawnow; %Updates graphical objects
figure(f1);
plot(f(1:end/2), 20*log10(Ya));
%STFT __ plots the whole audio signal after a stft, every 30ms
%% L,M,H - Bands
subplot(3,1,1)
y_low = Ya(f_LOW);
plot(f_LOW,y_low);
ylim([-20 60]);
title('Spektrum (LOW)');
xlabel('f(Hz)');
ylabel('dB');
grid on
subplot(3,1,2)
y_medium = Ya(f_MEDIUM);
plot(f_MEDIUM,y_medium);
ylim([-20 30]);
title('Spektrum (MEDIUM)');
xlabel('f(Hz)');
ylabel('dB');
grid on
subplot(3,1,3)
y_high = Ya(f_HIGH);
plot(f_HIGH,y_high);
ylim([-20 30]);
title('Spektrum (HIGH)');
xlabel('f(Hz)');
ylabel('dB');
grid on;
si=si+windowshift;
% start index updated
ei=ei+windowshift;
% end index updated
end

Answer 1

Here's the list of statements you could add to your code to generate the waterfall plot:
Let's store all STFT outputs in a matrix named Yb. Firstly, allocate the memory by adding this line before the for-loop.
Yb = NaN(N, fftlen/2);
Next, in the for-loop, save the fft result for each segment. This can be done by adding the following line after you have finished the computation of Ya (just before drawnow).
Yb(m,:) = Ya;
Now you're ready to generate the waterfall plot. This can be done by adding the following code after the end of the for-loop.
figure;
waterfall(f(f_LOW), (1:N)*windowshift/fs, Yb(:,f_LOW));
xlabel('Frequency (Hz)');
ylabel('Time (s)');
Hope this achieves what you want.
Following is not related to the main question: I also have the following suggestions to improve some other aspects of your code:
(1) The computation of the frequency grid f has a small scaling error. It should be:
f=f/fftlen*fs;
(2) Depending on the WAV file you use, your code may get fractional values in windowshift and N, but both of them need to be integers. So, use appropriate rounding methods while computing them. I'd suggest the following:
windowshift = round(segl/2);
N = floor(length(y)/windowshift);
(3) In the for-loop, you plot the whole fft only to overwrite that with the subplots immediately. That line should be removed.