Creating sounds with changing amplitude

I am trying to making sounds that simulate approaching noises. I want to create a 2 second 440 Hz sine wave that changes in amplitude (pure tone that gets louder over time). I need to get this change in amplitude two ways: 1) linearly where the change in amplitude is constant. And 2) where the change in amplitude is 1/((20*time)^2).

Is there a way to specify change in amplitude using equations? Thanks in advance.

Answer 1

[Star Strider]

Try this —

Fs = 44100;
Ft = 440;
sec = 2;
t = linspace(0, Fs*sec*60-1, Fs*sec*60).'/Fs;
% ChkFrq = 1/t(2)
s = sin(2*pi*Ft*t);

figure
plot(t, s)
grid
xlim([0 4410/Fs])                                    % 1 Seconds
xlabel('Time')
ylabel('Amplitude')
title('Original Signal')

s1 = s .* t/max(t);                                 % Increases Linearly From 1 To Zero Over 't'

figure
plot(t, s1)
grid
xlim([0 4410/Fs])                                   % 1 Seconds
xlabel('Time')
ylabel('Amplitude')
title('Linearly Increasing Signal')

s2 = s .* 20./((t.^2)+t(2));                        % This Envelope Will Clip

figure
plot(t, s2)
grid
xlim([0 4410/Fs])                                   % 1 Seconds
xlabel('Time')
ylabel('Amplitude')
title('Original Signal With Requested Envelope')

s3 = s .* (1/max(t)^2)/3./((t.^2)+t(2));             % This Envelope Will Not Clip

figure
plot(t, s3)
grid
xlim([0 4410/Fs])                                   % 1 Seconds
xlabel('Time')
ylabel('Amplitude')
title('Original Signal With Modified Envelope')

Fn = Fs/2;
L = numel(s);
NFFT = 2^nextpow2(L);
FTs = fft(s.*hann(L),NFFT)/L;
Fv = linspace(0, 1, NFFT/2+1)*Fn;
Iv = 1:numel(Fv);

figure
plot(Fv, abs(FTs(Iv))*2)
grid
xlim([400 500])
xlabel('Frequency (Hz)')
ylabel('Magnitude')
title('Fourier Transform')

These create column vectors, so use the sound function or the audioplayer function to listen to them.

EDIT — Corrected typographical errors.

.

[MARGARET]

Great code! If I am interested in making the same changes but in decibels instead of magnitude, how should I change the code to do that?

[Star Strider]

Thank you!

For the Fourier transform, the easiest way is:

plot(Fv, mag2db(abs(FTs(Iv))*2))

.

[MARGARET]

In the code you first posted with s3, how did you derive that from 1/((20*time)^2)? If I wanted to change the 20 value to 15, how would I do that? Thanks!

[Star Strider]

As always, my pleasure!

The ‘s3’ code is essentially a normalised version of ‘s2’ so that it will not clip or distort.

‘If I wanted to change the 20 value to 15, how would I do that?’

Change that value, and then use the normalize function with it to keep it from clipping.

Using the normalize function, specifically:

s3 = normalize(s2, 'range',[-1 1]);

and plotting that result in this version produces —

Fs = 44100;
Ft = 440;
sec = 2;
t = linspace(0, Fs*sec*60-1, Fs*sec*60).'/Fs;
% ChkFrq = 1/t(2)
s = sin(2*pi*Ft*t);

s2 = s .* 20./((t.^2)+t(2));                        % This Envelope Will Clip
s3 = normalize(s2, 'range',[-1 1]);                 % Will Not Clip When 'normalize' Used First 

figure
plot(t, s3)
grid
xlim([0 4410/Fs])                                   % 1 Seconds
xlabel('Time')
ylabel('Amplitude')
title('Original Signal With Requested Envelope, Normalized To [-1 1]')

to achieve the same result. The objective is to keep it from clipping the output, and distorting when played back.

.

Answer 2

[Image Analyst]

See attached demo where I vary both the pitch and amplitude of a sound waveform according to mathematical formulas.