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534 Chapter 9 SAMPLING RATE CONVERSION
P9.25 We want to design a linear-phase FIR filter to increase the input sampling rate by a factor
of 3 using the intfilt function.
1. Assuming full bandwidth of the signal to be interpolated, determine the impulse
response of the required FIR filter. Plot its amplitude response and the log-magnitude
response in dB. Experiment with the length parameter L to obtain a reasonable
stopband attenuation.
2. Assuming that bandwidth of the signal to be interpolated is π/2, determine the
impulse response of the required FIR filter. Plot its amplitude response and the
log-magnitude response in decibels. Again experiment with the length parameter L to
obtain a reasonable stopband attenuation.
P9.26 We want to design a linear-phase FIR filter to increase the input sampling rate by a factor
of 5 using the intfilt function.
1. Assuming full bandwidth of the signal to be interpolated, determine the impulse
response of the required FIR filter. Plot its amplitude response and the log-magnitude
response in decibels. Experiment with the length parameter L to obtain a reasonable
stopband attenuation.
2. Assuming that bandwidth of the signal to be interpolated is 4π/5, determine the
impulse response of the required FIR filter. Plot its amplitude response and the
log-magnitude response in decibels. Again experiment with the length parameter L to
obtain a reasonable stopband attenuation.
P9.27 Using the Parks-McClellan algorithm, design an interpolator that increases the input
sampling rate by a factor of I =2.
1. Determine the coefficients of the FIR filter that has 0.5 dB ripple in the passband and
50 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. Let x(n) =cos(0.4πn). Generate 100 samples of x(n), and process it using this filter to
interpolate by I =2to obtain y(m). Provide the stem plots of the both sequences.
P9.28 Using the Parks-McClellan algorithm, design an interpolator that increases the input
sampling rate by a factor of I =3.
1. 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. Determine the corresponding polyphase structure for implementing the filter.
4. Let x(n) =cos(0.3πn). 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.
P9.29 A signal x(n) istobeinterpolated by a factor of 3. It has a bandwidth of 0.4π, but we
want to preserve frequency band up to 0.3π 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 0.1 dB ripple in the passband and
40 dB attenuation in the stopband.
2. Provide plots of the impulse and the log-magnitude responses.
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