# How to create sounds with specific characteristics?

29 views (last 30 days)
D. on 31 May 2011
Commented: Ilya Rotov on 10 Oct 2020
How can I create sounds with MATLAB with the following characteristics:
Sound 1:
pitch: 3 sinusoidal partials of 500, 1000 and 1500 Hz
duration: 100 ms (including 5 ms rise and fall times)
amplitude: 80 dB
Sound 2:
like Sound 1, but with a cutting out of 10 ms (5 ms fall / rise included) from the middle of the sound
This is my third try ( adapted from http://www.music.mcgill.ca/~gary/307/week1/matlab.html ):
%%configure signal settings
duration = 0.1; % duration in seconds
amplitude = 0.8; % amplitude
f1 = 500; % frequency in Hertz
f2 = 1000;
f3 = 1500;
phi = 2*pi*0.5; % phase offset, e.g.: 2*pi*0.25 = 1/4 cycle
%%configure output settings
fs = 44100; % sampling rate
T = 1/fs; % sampling period
t = 0:T:duration; % time vector
%%create the signal
omega1 = 2*pi*f1; % angular frequency in radians
omega2 = 2*pi*f2;
omega3 = 2*pi*f3;
partial1 = cos(omega1*t + phi)*amplitude; % sinusoidal partial 1
partial2 = cos(omega2*t + phi)*amplitude; % sinusoidal partial 2
partial3 = cos(omega3*t + phi)*amplitude; % sinusoidal partial 3
signal = (partial1 + partial2 + partial3)/3;
%%plot the signal
plot(t, signal);
xlabel('Time (seconds)');
ylabel('Amplitude');
title('Complex Signal');
%%play the signal
sound(signal, fs);
%%save signal as stereo wave file
stereo_signal = [x1; x1]';
wavwrite(stereo_signal, fs, 'test.wav');
I am wondering how to adjust the amplitude and to implement the rise and fall.
Ilya Rotov on 10 Oct 2020
Obvious understanding. Thanks!

Ivan van der Kroon on 1 Jun 2011
A window can be anything going from zero to unity. In this case it should reach unity after 5ms from the start. You should know what kind of performance you are looking for, so you can determine what response your window should have.
Often I start with 1/4 of a sine period, since it has the nice properties to start with a ramp and that its derivative is continuous when it meets unity. For instance for time array t with begin time b and end time e of the window;
w = ((1+sin(pi*(t-b)/2/e))/2.*(t>b-e)-1 ) .*(t<=b+e)+ 1;
This equals 0 for t<b, then increases and equals 1 for t>e. Also note that Matlab has a large number of windows available.
And note that the way you're implementing the amplitudes is very different form the decibels you specify!