How to create sounds with specific characteristics?

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.

Looking forward to your help! Thanks in advance!

[Daniel Shub]

How do you want to the signal to rise/fall? Probably a raised cosine (hanning or hamming window).

80 dB re what? It cannot be 80 dB SPL without knowing your speaker and amplifier.

[D.]

Thank you for your answer!

OK, i set a factor for my amplitude (0.8). I should generate another sound with 100 dB. Does it make sense to set the amplitude to 1 then?

I thought, I could adjust an amplifier to 100 dB on the second file and then play the first sound with factor 0.8 to have 80 dB.

For the window function I have to read a bit, because I don't understand this, yet.

[John]

THANK YOU!

[Ilya Rotov]

Obvious understanding. Thanks!

Answer 1

[Ivan van der Kroon]

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!