Question

If z₀ is a zero of a (real-valued) linear - phase FIR filter then following is/are also zero/zeros of a (real-valued) linear - phases FIR filter,
1. \(z_0^*\)
2. \(\frac{1}{{{z_0}}}\)
3. \(\frac{1}{{{z_0}}}\), \(z_0^*\) and \(\frac{1}{{z_0^*}}\)
4. \(\frac{1}{{{z_0}}}\) and \(\frac{1}{{z_0^*}}\)

Answer 1

Correct Answer - Option 3 : \(\frac{1}{{{z_0}}}\), \(z_0^*\) and \(\frac{1}{{z_0^*}}\)

Concept:

In the case of linear phase FIR filter, to have a one zero, z = 0 as z0 other zeros are.

\({z_0},\frac{1}{{{z_0}}},\left[ {z_0^*} \right],{\left[ {\frac{1}{{{z_0}}}} \right]^*}\)

For example:

z₀ = 3 + 4j

\(\left[ {z_0^*} \right] = 3 - 4j\)

\(\frac{1}{{{z_0}}} = \frac{1}{{3 + 4j}} = \frac{{3 - j4}}{{25}} = \frac{3}{{25}} - \frac{{j4}}{{25}}\)

\({\left[ {\frac{1}{{{z_0}}}} \right]^*} = \frac{3}{{2j}} + j\frac{4}{{25}}\)

IIR Filters	FIR filters
1. IIR filters are difficult to control and have no particular phase.	1. FIR filters make a linear phase always possible.
2. IIR can be unstable.	2. FIR is always stable.
3. IIR filters are used for applications that are not linear.	3. FIR filters are dependent upon linear-phase characteristics.
4. IIR filters are dependent on both i / p and o / p.	4. FIR is dependent upon i / p only
5. IIR filters consist of zeros and poles and require less memory than FIR filters.	5. FIR only consists of zeros so they require more memory.
6. Where the system response is infinite, we use IIR filters.	6. where the system response is zero, we use FIR filters.
7. IIR filters are recursive, and feedback is also involved.	7. FIR filters are non-recursive and no feedback is involved.