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536 Chapter 9 SAMPLING RATE CONVERSION
4. Using the fir2 function, generate a 151-length sequence x 2(n) whose frequency-domain
sampled values are 1 at ω =0,0.9 at ω =0.2π, 1atω =0.4π, 0.5 at ω =0.45π, 0at
ω =0.5π, and0atω = π. Process x 2(n), using this filter to decimate it by a factor of 2
to obtain y 2(m). Provide the spectral plots of both sequences.
P9.34 A signal x(n) istobedecimated by a factor of D =3.Ithas a bandwidth of 0.25π, and we
will tolerate aliasing this frequency 0.3π 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
40 dB attenuation in the stopband.
2. Provide plots of the impulse and the log-magnitude responses.
3. Let x 1(n) =cos(0.2πn)+2sin(0.3πn). Generate 300 samples of x 1(n), and process it
using this filter to decimate by D =3to obtain y 1(m). Provide the stem plots of both
sequences.
4. Using the fir2 function, generate a 151-length sequence x 2(n) whose frequency-domain
sampled values are 1 at ω =0,1atω =0.1π, 1atω =0.25π, 0.5 at ω =0.3π, 0at
ω =0.35π, and 0 at ω = π. Process x 2(n), using this filter to decimate it by a factor of
3toobtain y 2(m). Provide the spectral plots of both sequences.
P9.35 Design a sampling rate converter that reduces the sampling rate by a factor of 2/5.
1. Using the Parks-McClellan algorithm, 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. Specify the sets of the time-varying coefficients g(m, n) and the corresponding
coefficients in the polyphase filter realization.
4. Let x(n) =sin(0.35πn)+2cos(0.45πn). Generate 500 samples of x(n) and process it
using this filter to resample by 2/5 toobtain y(m). Provide the stem plots of both
sequences.
P9.36 Design a sampling rate converter that increases the sampling rate by a factor of 7/4.
1. Using the Parks-McClellan algorithm, determine the coefficients of the FIR filter that
has 0.1 dB ripple in the passband and 40 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. Specify the sets of the time-varying coefficients g(m, n) and the corresponding
coefficients in the polyphase filter realization.
4. Let x(n) =2sin(0.35πn)+cos(0.95πn). Generate 500 samples of x(n) and process it,
using this filter to resample by 7/4 toobtain y(m). Provide the stem plots of both
sequences.
P9.37 A signal x(n) istoberesampled by a factor of 3/2. It has a total bandwidth of 0.8π, but
we want to preserve frequencies only up to 0.6π and require that the band up to 0.75π be
free of aliasing in the resampled signal.
1. Using the Parks-McClellan algorithm, 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.
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