Question

Let 3 + 4j be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is

1. 3 – 4j
2. \(\frac{3}{{25}} + \frac{4}{{25}}j\)
3. \(\frac{3}{{25}} - \frac{4}{{25}}j\)
4. \(\frac{1}{3} - \frac{1}{4}j\)

Answer 1

Correct Answer - Option 4 : \(\frac{1}{3} - \frac{1}{4}j\)

Concept:

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

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

Analysis:

Z₀ = 3 + 4j

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

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

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