How to get equation of a sound

I would like to get the equation for the next sound of piano keys (I have attached the zip with the mp3 file):

By equation I mean the formula of the general trend of the sound. To get the graph above I used the following code:

[x, fs] = audioread("IA de Mate\The Lumineers - April (Part 9 Of 10).mp3")

X = x(:,1);

N = length(x);
t = (0:N-1)/fs;
N/fs

%plot time domain signa
plot(t, x)
grid on 
xlabel('time(s)')
ylabel('amplitude')
title('Signal in Time Domain')

[Walter Roberson]

What would an example formula be?

[Luis Zuniga]

Something like f(x) = sin(x)

Although of course, for the sound y have attached is probably going to be something a bit more complex

[KSSV]

Use fft; you will get many frequencies as your signal is random. fft gives amplitude and frequecny. Sum all these you shall get your equation.

[Tamir Suliman]

I thnk you may use or could use https://www.mathworks.com/help/matlab/ref/polyfit.html

to get the equations

[KSSV]

@Tamir Suliman: the signal is random, you cannot use polyfit for this.

Answer 1

[Madhav Thakker]

Hi Luis,

I understand that you want to get the equation of the attached mp3 file. The attached signal is very random. However, you can get a non-intuitive complex equation by using fft in MATLAB.

I am attaching a snippet that might help you –

[x, fs] = audioread("The Lumineers - April (Part 9 Of 10).mp3");
L = numel(x(:,1));
Fn = fs/2;                                          % Nyquist Frequency
xm = x-mean(x);                                     % Subtract Mean To Make Amplitudes At Frequencies>0 More Prominent
FTs = fft(xm)/L;                                    % Fourier Transform
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                 % Frequency Vector
Iv = 1:length(Fv);                                  % Index Vector
Phs = angle(FTs);

For more details, you can refer to a similar discussion here - https://www.mathworks.com/matlabcentral/answers/348847-how-to-get-equation-of-signal-in-matlab

Hope this helps.