Sine wave changing amplitude

Can you have a sine wave with varying amplitudes? I think this concept does not exist.

Answer 1

[Image Analyst]

See attached demo (make_wav_file.m, below the plot) where I vary the amplitude and frequency of a sound wave.

[Tahariet Sharon]

Yes, but the initial qustion was about changing the amplitude of a SINE wave, not a complex wave.

[Image Analyst]

My demo DOES modify the amplitude of a sine wave. Perhaps you overlooked this line of code in it:

% Construct the waveform:
y = int16(Amplitude .* sin(2.*pi.*t./T));

The amplitude array is changing according to 2 ways in my demo: an exponential decay and another lower frequency since wave, but you could alter the amplitude in whatever way you want. So I'm not sure why the "but" is in your comment.

Answer 2

[Orion]

Sure you can.

a sine wave is defined by

y = A*sin(w*t+phi).

if you define A as a function(vector) dependant of the time, then you get a sine wave with varying amplitudes.

t = 0:0.01:10;
w = 8*pi;
phi = 0;

A = floor(t); % why not

y = A.*sin(w*t+phi);
plot(t,y);

I did it in matlab, but you can obviously do it with simulink (don't know what tool you're using).

[chirag hb]

 Can u tell when me how to do in simulink

Answer 3

[Youssef Khmou]

Nuchto, That is the amplitude modulation, it is possible to simulate that type of signals:

 x=real(exp(j*2*pi*(0:0.1:10)));
 y=rand(size(x)).*x;

 subplot(1,2,1), plot(x);
 subplot(1,2,2); plot(y): title(' random amplitude');

[Nuchto]

Thanks, but once we mix two sine waves, it's a complex wave, isn't it? So it's not anymore a sine wave, it can be decomposed using FFT into two.

[Youssef Khmou]

no, and fft is always complex.

[Image Analyst]

But sometimes the imaginary part is zero. Here is the table:

Time Domain    Frequency Domain
real      hermitian (real=even, imag=odd)
imaginary    anti-hermitian (real=odd, imag=even)
even      even
odd      odd
real and even    real and even (i.e. cosine transform)
real and odd    imaginary and odd (i.e. sine transform)
imaginary and even  imaginary and even
imaginary and odd  real and odd

[Youssef Khmou]

Ok