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Some digital filters are based on the Fast Fourier Transform (FFT). As discussed,
the FFT is a mathematical algorithm that quickly extracts the frequency domain of
the signal, allowing the spectrum to be manipulated to create filtering. When the
filtering is done, the inverse FFT operation is used to convert back to the time
domain.
Digital filters are becoming popular in modern radio communications. Digital filters
are also widely used outside of radio communications. You can find digital filters in
almost any electronic system where analogue filters were used. Digital filters are
often used in conjunction with analogue filters.
Digital filters are divided into the following two categories:

Infinite impulse response (IIR)
Finite impulse response (FIR)

As the names suggest, each type of filter is categorised by the length of its impulse
response. By far the most common filter is the FIR. Finite impulse response (FIR)
filters are the most popular type of filters implemented in software.
FIR filters have a linear phase response and are therefore the most suitable type for
radio communications.

Digital filters are implemented in software or specialised hardware. If we were to
draw a block diagram of an FIR filter, what we would really be drawing is a
mathematical process. You can’t “look at” or “hold” a digital filter as you can an
analogue one. If you are building an analogue filter, you would think about a physical
construction using components some mounting structure and you would reach for
the soldering iron.
If you were to design a digital filter, you would reach for specialised design software
or a computer with “C”, Python etc. We could implement the digital filter using an
FPGA or other specialised firmware.
If you are like me, you will just enjoy the adjustable digital filters in your SDR
transceiver and leave the design to software/communications engineers.

WHAT IS AN FPGA?
FPGAs belong to a class of devices known as programmable logic, or sometimes
referred to as programmable hardware. Essentially, an FPGA doesn’t do anything
itself but it can be configured to be just about any digital circuit you want.
The magic here is that nothing physically changes. You simply load a configuration
into the FPGA and it starts behaving like the circuit you wanted. No soldering, no
jumper wires, no fuss. An FPGA can then be reconfigured to behave like another
circuit, and another, and another. The configuration is RAM based which means it
can essentially be reconfigured an unlimited number of times.

Even though we talk about using FPGAs to create digital circuits, you don’t draw
circuit schematics to create designs for them.
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