Understanding the lowpass filtering of a digital signal I do not have any background in Electrical Engineering and I have recently started a project which involves signals captured from sensors.

Lowpass filtering: The way I understand it is: The values below the CUTOFF are allowed to pass through, above the CUTOFF are simply filtered.

So far so good. Now, how does this work in real world?

The data I have is captured 100 times per second at equidistant intervals, hence my sampling frequency is 100 Hz. This is also understandable. 

But now, my CUTOFF is 20 Hz. What does it mean? Because all I have is some digits. None of them is below 20. When I read about filtering it makes me think of CUTOFF as some value from the range of signal itself. I have given multiple explanations to myself. 


Somehow, from the signal, find out the frequency of each data point and if that frequency is below 20 Hz, don't do anything. Otherwise put 20 Hz in the output. But I have no idea how to find out frequency of single data point. After all, its just a number, right?
It has to work on multiple values at a time. That is, from one data point to the other, if there is some above average peak, just smooth it out. And this 20 Hz is essentially a limit of how sharp the peak can be.


Please help me understand in the simplest terms. I asked the same question to my guide and he explained me using the terminologies in Electrical Engineering and some more alienate stuff, which was ways and bounds beyond my brain.
Any signal can be constructed from the sum of sinusoids of different frequencies (to within an arbitrarily small error).  This reconstruction is unique and can be calculated with the Fourier transform.

When we talk about the various frequencies that comprise a signal, we are talking about these sinusoids of various frequencies.  In fact, in signal processing, we are used to thinking about the same signal in the time domain -- as a function that gives a magnitude for every instant in time, or in the frequency domain -- as a function that gives a magnitude and phase for every frequency.

When you apply a low-pass filter, you are modifying the frequency domain view of the signal so that all frequencies higherthan the cutoff have their magnitudes set to pretty much zero.

Another way of thinking about it is, you take all the sinusoids that make up the original signal, and throw away the ones with frequency higher than your cutoff.

The secret to how this actually works is called the "convolution theorem": https://en.wikipedia.org/wiki/Convolution_theorem

The convolution theorem shows that convolving two signals together is the same as multiplying their frequency-domain representations together.  A "low pass" filter is just a signal that has a constant magnitude for frequencies below the cutoff, and near zero magnitude for frequencies above the cutoff.

When the filter is convolved with the input signal, the input signal's high-frequency components are multiplied by zero, effectively removing them.