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