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Which one of the following refers to the frequency ωk in the frequency response of an FIR filter?
1. \(\frac{{16\pi }}{M}\left( {k + \alpha } \right)\)
2. \(\frac{{8\pi }}{M}\left( {K + \alpha } \right)\)
3. \(\frac{{4\pi }}{M}\left( {k + \alpha } \right)\)
4. \(\frac{{2\pi }}{M}\left( {k + \alpha } \right)\)

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Correct Answer - Option 4 : \(\frac{{2\pi }}{M}\left( {k + \alpha } \right)\)

Frequency sampling structure is used for the realization of FIR (Finite Impulse Response) filter.

In this structure, a set of equally spaced frequencies is used to get the desired frequency response.

This set of frequencies is defined as:

\({\omega _k} = \frac{{2\pi }}{M}\left( {k + \alpha } \right)\)  

\(k = 0,\;1,\;2,\; \ldots \frac{{M - 1}}{2}\) for M = odd

\(k = 0,\;1,\;2,\; \ldots \frac{M}{2} - 1\) for M = even

α = 0 or \(\frac{1}{2}\)

Note:

There are four types of structure is used for the realization of the FIR filter.

i) Direct-form structure

ii) Cascade form structure

iii) Frequency sampling structure

iv) Lattice structure

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