Test: Optimum Equiripple Filter Design - 1 - Electronics and Communication Engineering (ECE) MCQ

Explanation: The filter design method described in the design of optimum equi ripple linear phase FIR filters is formulated as a chebyshev approximation problem.

If the filter has anti-symmetric unit sample response with M even, then what is the value of Q(ω)?
a) cos(ω/2)
b) sin(ω/2)
c) 1
d) sinω

Explanation: The weighting function on the approximation error allows to choose the relative size of the errors in the different frequency bands. In particular, it is convenient to normalize W(ω) to unity in the stop band and set W(ω)=δ2/ δ1 in the pass band.

Explanation: The weighted approximation error is defined as E(ω) which is given as
E(ω)= W(ω)[H_dr(ω)- H_r(ω)].

Explanation: The error function E(ω) alternates in sign between two successive extremal frequency, Hence the theorem is called as Alternative theorem.

Explanation: We know that we can have at most L-1 local maxima and minima in the open interval 0<ω<π. In addition, ω=0 and π are also usually extrema. It is also maximum at ω for pass band and stop band frequencies. Thus the error function of a low pass filter has at most L+3 extremal frequencies.

Explanation: In general, the filter designs that contain more than L+2 alternations or ripples are called as Extra ripple filters.

Explanation: Having the solution for P(ω), we can now compute the error function E(ω) from
E(ω)= W(ω)[H_dr(ω)- H_r(ω)] on a dense set of frequency points. Usually, a number of points equal to 16M, where M is the length of the filter.

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

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