Digital Filters Design MCQ [Free PDF] – Objective Question Answer for Digital Filters Design Quiz

The value of JTYPE=3 in the Parks-McClellan program to select a filter that performs Hilbert transformer.

In the Parks-McClellan program, LGRID represents the grid density for interpolating the error function. The default value is 16 if left unspecified.

FX denotes an array of maximum size 10 that specifies the desired frequency response in each band.

Let us consider the design of a low pass filter with the passband edge frequency ωP and the ripple in the pass band is δ1, then from the general specifications of the Chebyshev filter, in the passband the filter frequency response should satisfy the condition
1- δ1 ≤ Hr(ω) ≤ 1+δ1; |ω|≤ωP

If the filter has a symmetric unit sample response, then we know that
h(n)=h(M-1-n)
and for M odd in this case, Q(ω)=1.

If the filter has a anti-symmetric unit sample response, then we know that
h(n)= -h(M-1-n)
and for M odd in this case, Q(ω)=sin(ω).

164. In which of the following way the real-valued desired frequency response is defined?

A. Unity in stopband and zero in passband
B. Unity in both pass and stop bands
C. Unity in passband and zero in stop band
D. Zero in both stop and pass band

Show Explanation

The real-valued desired frequency response Hdr(ω) is simply defined to be unity in the pass band and zero in the stopband.

According to the Alternation theorem, a necessary and sufficient condition for P(ω) to be a unique, best-weighted Chebyshev approximation, is that the error function E(ω) must exhibit at least L+2 extremal frequencies in S.

In general, the filter designs that contain a maximum number of alternations or ripples are called maximal ripple filters.

Initially, we neither know the set of external frequencies nor the parameters. To solve for the parameters, we use an iterative algorithm called the Remez exchange algorithm, in which we begin by guessing at the set of extremal frequencies.

|E(ω)|≥δ for some frequencies on the dense set, then a new set of frequencies corresponding to the L+2 largest peaks of |E(ω)| are selected and computation is repeated.

Since the new set of L+2 extremal frequencies is selected to increase in each iteration until it converges to the upper bound, this implies that when |E(ω)|≤δ for all frequencies on the dense set, the optimal solution has been found in terms of the polynomial H(ω).

FX denotes an array of maximum size 10 that specifies the weight function in each band.

The Chebyshev approximation problem is viewed as an optimum design criterion in the sense that the weighted approximation error between the desired frequency response and the actual frequency response is spread evenly across the pass band and evenly across the stopband of the filter minimizing the maximum error. The resulting filter designs have ripples in both the passband and stopband.

If the filter has a symmetric unit sample response, then we know that
h(n)=h(M-1-n)
and for M even in this case, Q(ω)=cos(ω/2).

An ideal differentiator has a frequency response that is linearly proportional to the frequency.

An ideal differentiator is defined as one that has the frequency response
Hd(ω)= jω ; -π ≤ ω ≤ π.

We know that, for an ideal differentiator, the frequency response is given as
Hd(ω)= jω ; -π ≤ ω ≤ π
Thus, we get the unit sample response corresponding to the ideal differentiator is given as
h(n)=cos⁡πn/n

We know that the unit sample response of an ideal differentiator is given as
cos⁡πn/n
So, we can state that the unit sample response of an ideal differentiator is anti-symmetric because cos⁡πn is also an anti-symmetric function.

Since we know that the unit sample response of an ideal differentiator is anti-symmetric,
=>hd(0)=0.