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FIR filters are most stable as compared with IIR filters due to its non feedback nature.

**Features of FIR Filter**

1.
FIR filter always provides linear phase response.
This specifies that the signals in the pass band will suffer no dispersion
Hence when the user wants no phase distortion, then FIR filters are preferable
over IIR. Phase distortion always degrade the system performance. In various
applications like speech processing, data transmission over long distance FIR
filters are more preferable due to this characteristic.

2.
FIR filters are most stable as compared with IIR
filters due to its non feedback nature.

3.
Quantization Noise can be made negligible in FIR
filters. Due to this sharp cutoff FIR filters can be easily designed.

4.
Disadvantage of FIR filters is that they need
higher ordered for similar magnitude response of IIR filters.

**FIR SYSTEM ARE ALWAYS STABLE. Why?**

Proof:

Difference equation of FIR filter of length M
is given as

And the coefficient bk are related to unit
sample response as

H(n) = bn for 0 ≤ n ≤ M-1

= 0 otherwise.

We can expand this equation as

Y(n)= b0 x(n) + b1 x(n-1) + …….. + bM-1
x(n-M+1) (2)

System is
stable only if system produces bounded output for every bounded input. This is
stability definition for any system.

Here
h(n)={b0, b1, b2, } of the FIR filter are stable. Thus y(n) is bounded if input
x(n) is bounded. This means FIR system produces bounded output for every
bounded input. Hence FIR systems are always stable.

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