Re: fir filters
text2babu,
It is true that the FIR filter has no poles, since it consists of weighted delayed sums of the input samples. However, the FIR filter can be designed to have desired properties, Low Pass, High Pass, etc.
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It is also true the FIR filters are always stable. However, IIR filters can be designed to be stable. The only requirement is that the poles of the IIR filter all lie within the region of convergence, e.g., a circle of radius one for normalized filters.
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The symmetry requirements that you mention are criteria for phase linearity, not stability. FIR filters are stable regardless of this symmetry property.
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See any book on DSP for further details.
Regards,
Kral