2.2 Audio Signals - Sine

On this site you can generate a sine signal, overlay it with a noise and watch, how the function changes. By using the FFT the frequency spectrum is produced. Now you can work with filters to reconstruct the strating signal after IFFT calculation.
The FFT and IFFT calculations are carried out by NumPy, a free software for computating numerical problems, on a server. This calculation might take a few minutes.
This image shows a sine function.
By moving the frequency controller (red) an appropriate sine signal can be generated and heard.
Now the standard pitch a’ is given with the frequency
ν = 440 Hz.
The graph is a function of time.

Note:
The audio signal lasts two seconds. For better clarity only a part of 0.5 seconds is shown.
The sine oscillation looks unregular for some frequencies erroneously, because only shown a selection of certain values is presented for reasons of speed.

Multiplicating this sine with an accident function (Math.random function) results in a disturbance of the audio signal, which is audible as a noise.
You can also see, that the sine is not regular any more.
The graph is still a function of time.


After clicking on the button "FFT calculation" the frequency spectrum of the sine signal is shown.
So a function of frequency has been produced out of the function of time. Now you can see the signal′s frequencies with the absolute values of the Fourier transformed.

By moving the appropriate controllers (red) the frequencies, that shall be filtered, (horizontal controllers: bass and treble filter) as well as the intensity of filtration (vertical controller) can be varied.


By clicking on the button "IFFT calculation" the appropriate sine signal is generated out of the filtered frequency spectrum and can be viewed.
The graph is a function of time.

The aim should be to remove the noise so the starting signal is reconstructed as well as possible.