UploadFile_6417

Problems 535
3. Let x(n) =cos(0.3πn)+0.5 sin(0.4πn). Generate 100 samples of x(n), and process it
using this filter to interpolate by I =3to obtain y(m). Provide the stem plots of both
sequences.
P9.30 A signal x(n) istobeinterpolated by a factor of 4. It has a bandwidth of 0.7π, but we
want to preserve frequency band up to 0.6π in the interpolated signal. Using the
Parks-McClellan algorithm, we want to design such an interpolator.
1. Determine the coefficients of the FIR filter that has 0.5 dB ripple in the passband and
50 dB attenuation in the stopband.
2. Provide plots of the impulse and the log-magnitude responses.
3. Let x(n) =sin(0.5πn)+cos(0.7πn). Generate 100 samples of x(n) and process it using
this filter to interpolate by I =4to obtain y(m). Provide the stem plots of both
sequences.
P9.31 Using the Parks-McClellan algorithm, design a decimator that downsamples an input
signal x(n) byafactor of D =5.
1. Determine the coefficients of the FIR filter that has 0.1 dB ripple in the passband and
30 dB attenuation in the stopband. Choose reasonable values for the band-edge
frequencies.
2. Provide plots of the impulse and the log-magnitude responses.
3. Determine the corresponding polyphase structure for implementing the filter.
4. Using the fir2 function, generate a 131-length sequence x(n) whose frequency-domain
sampled values are 1 at ω =0,0.9 at ω =0.1π, 1atω =0.2π, 1atω =0.5π, 0.5 at
ω =0.55π, 0atω =0.6π, and0atω = π. Process x(n) using this filter to decimate it
by a factor of 5 to obtain y(m). Provide the spectral plots of both sequences.
P9.32 Using the Parks-McClellan algorithm, design a decimator that downsamples an input
signal x(n) byafactor of D =3.
1. Determine the coefficients of the FIR filter that has 0.5 dB ripple in the passband and
30 dB attenuation in the stopband. Choose reasonable values for the band-edge
frequencies.
2. Provide plots of the impulse and the log-magnitude responses.
3. Let x 1(n) =sin(0.2πn)+0.2 cos(0.5πn). Generate 500 samples of x 1(n), and process it
using this to decimate by D =3to obtain y 1(m). Provide the stem plots of both
sequences.
4. Using the fir2 function, generate a 131-length sequence x 2(n) whose frequency-domain
sampled values are 1 at ω =0,0.8 at ω =0.15π, 1atω =0.3π, 1atω =0.4π, 0.5 at
ω =0.45π, 0atω =0.5π, and 0 at ω = π. Process x 2(n), using this filter to decimate it
by a factor of 3 to obtain y 2(m). Provide the spectral plots of both sequences.
P9.33 A signal x(n) istobedecimated by a factor of D =2.Ithas a bandwidth of 0.4π, and we
will tolerate aliasing this frequency 0.45π in the decimated signal. Using the
Parks-McClellan algorithm, we want to design such a decimator.
1. Determine the coefficients of the FIR filter that has 0.1 dB ripple in the passband and
45 dB attenuation in the stopband.
2. Provide plots of the impulse and the log-magnitude responses.
3. Let x 1(n) =cos(0.4πn)+2sin(0.45πn). Generate 200 samples of x 1(n), and process it
using this filter to decimate by D =2to obtain y 1(m). Provide the stem plots of both
sequences.
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.