UploadFile_6417

Problems 381
2.02
1.98
Hr(ω)
1
0
0
0.25 0.35 0.65 0.75 1
ω
π
FIGURE P7.1 Filter Specifications for Problem P7.27
}
lower passband edge = 0.4π
R
upper passband edge = 0.6π p =0.5 dB.
Provide a plot of the log-magnitude response in dB and stem plot of the impulse response.
P7.29 The frequency response of an ideal bandpass filter is given by
{ 0, 0 ≤|ω| ≤ π/3
H d (e jω )= 1, π/3 ≤|ω| ≤ 2π/3
0, 2π/3 ≤|ω| ≤ π
1. Determine the coefficients of a 25-tap filter based on the Parks-McClellan algorithm
with stopband attenuation of 50 dB. The designed filter should have the smallest
possible transition width.
2. Plot the amplitude response of the filter using the function developed in Problem P7.6.
P7.30 Consider the bandstop filter given in Problem P7.10.
1. Design a linear-phase bandstop FIR filter using the Parks-McClellan algorithm. Note
that the length of the filter must be odd. Provide a plot of the impulse response and the
magnitude response in dB of the designed filter.
2. Plot the amplitude response of the designed filter and count the total number of extrema
in stopband and passbands. Verify this number with the theoretical estimate of the total
number of extrema.
3. Compare the order of this filter with those of the filters in Problems P7.10 and P7.24.
4. Verify the operation of the designed filter on the following signal
x(n) =5− 5 cos
( πn
2
)
; 0 ≤ n ≤ 300
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.