Time, why you punish me?
Viewing information in time domain is something that is present in many fields of science and technology. It is not so clear that there are
other domains through which we can gain insight on information. One such "hidden" domain is; frequency domain.
In order to analyze a signal in frequency domain, it must undergo what is known as a transformation which converts its values into another
form. In the case of this blog post, the transformation we will be looking at is called the Fourier Transform. In this case, we are using a computer
which is by nature a discrete device - the discrete transform must be used.
The whole essence of the fourier transform is asking of a signal, what frequencies exist? What periodic oscillations exist in the given signal?
Specifically, what sinusoids (at some given frequency) are present?
Without bothering with the math too much, we can do this by multiplying by different sinusoids and comparing them. This can then be visualized
as "magnitude" plotted over "frequency", where "magnitude" means the strength of a sinusoid at a specific frequency.
In the example below, there is a sinusoid at a given frequency that lasts for 2 seconds. If you switch to frequency domain, you can see there are
two peaks, one in the positive side (real) and one on the negative side (imaginary). It turns out that negative frequencies are important for the
mathematics, but not present in real life.
NOTE that this signal has noise added to it and is finite in length. This creates spread out peaks and a noisy floor.
You can use the buttons above to switch between frequency domain and time domain - or generate a new signal.
That's it for now - this has been mostly an experiment to show what a simple sinusoid looks like in frequency domain using js.
Be Curious!
© 2020 Sky Hoffert