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Which of the following filter design is used in the formulation of design of optimum equi ripple linear phase FIR filter?
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 antisymmetric unit sample response with M even, then what is the value of Q(ω)?
If the filter has antisymmetric 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
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 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.
Which of the following defines the weighted approximation error?
Explanation: The weighted approximation error is defined as E(ω) which is given as
E(ω)= W(ω)[H_{dr}(ω) H_{r}(ω)].
The error function E(ω) does not alternate in sign between two successive extremal frequencies.
Explanation: The error function E(ω) alternates in sign between two successive extremal frequency, Hence the theorem is called as Alternative theorem.
At most how many extremal frequencies can be there in the error function of ideal low pass filter?
Explanation: We know that we can have at most L1 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.
The filter designs that contain more than L+2 alternations are called as:
Explanation: In general, the filter designs that contain more than L+2 alternations or ripples are called as Extra ripple filters.
If M is the length of the filter, then at how many number of points, the error function is computed?
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.
What is the value of JTYPE in the ParksMcClellan program for a Hilbert transformer?
Explanation: The value of JTYPE=3 in the ParksMcClellan program to select a filter that performs Hilbert transformer.
In ParksMcClellan program, the grid density for interpolating the error function is denoted by which of the following functions?
Explanation: In ParksMcClellan program, LGRID represents the grid density for interpolating the error function. The default value is 16 if left unspecified.
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