Finite impulse response filters are always stable and can have linear phase.
y[n]=Σb_k x[n-k]: no feedback, always stable, can have exactly linear phase (symmetric coefficients), but needs many taps for sharp transitions. Design by windowing, frequency sampling or Parks-McClellan equiripple. Implemented with MAC operations.
A 101-tap FIR can make a sharp audio low-pass without phase distortion.
FIR filters are always stable and can have exactly linear phase, which makes them valued for audio, communication and measurement.
Finite impulse response filters are always stable and can have linear phase.
FIR filters are always stable and can have exactly linear phase, which makes them valued for audio, communication and measurement.
They have no feedback, so the output depends only on a finite set of past inputs and cannot grow without limit.
To achieve a sharp transition, the impulse response must be long, so FIR filters often require many more coefficients than IIR designs.
Typical applications include filtering audio without distorting the timing of speech, designing a receiver filter that must not shift signal phase and implementing a simple moving average to smooth sensor data.
Study "Z-transform" first (topic 30 of 101 in Signals, Control & Comms). It covers the groundwork this topic builds on.
Linear phase. Group delay (N-1)/2. Order estimation.
A 101-tap FIR can make a sharp audio low-pass without phase distortion.
The next topic is "IIR filters", which builds directly on this one.
It is classed as Beginner in Signals, Control & Comms (topic 31 of 101). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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