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532 Chapter 9 SAMPLING RATE CONVERSION
P9.11 Using the fir2 function, generate a 101-length sequence x(n) whose frequency-domain
sampled values are 0.5 at ω =0,1atω =0.1π, 1atω =0.2, 0atω =0.22π, and0at
ω = π.
1. Compute and plot the DTFT of x(n).
2. Decimate x(n) byafactor of 2, and plot the DTFT of the resulting sequence.
3. Decimate x(n) byafactor of 4, and plot the DTFT of the resulting sequence.
4. Decimate x(n) byafactor of 5, and plot the DTFT of the resulting sequence.
5. Comment on your results.
P9.12 Using the function upsample, study the operation of factor-of-4 upsampling on the
following sequences. Use the stem function to plot the original and the upsampled
sequences. Experiment using the default offset value of zero and the offset value
equal to 2.
1. x 1(n) =sin(0.6πn), 0 ≤ n ≤ 100
2. x 2(n) =sin(0.8πn)+cos(0.5πn), 0 ≤ n ≤ 100
3. x 3(n) =1+cos(πn), 0 ≤ n ≤ 100
4. x 4(n) =0.2 n, 0 ≤ n ≤ 100
5. x 5(n) ={1, 1, 1, 1, 0, 0, 0, 0, 0, 0} PERIODIC, 0 ≤ n ≤ 100
P9.13 Using the fir2 function, generate a 91-length sequence x(n) whose frequency-domain
sampled values are 0 at ω =0,0.5 at ω =0.1π, 1atω =0.2, 1atω =0.7π, 0.5 at
ω =0.75π, 0atω =0.8π, and0atω = π.
1. Compute and plot the DTFT magnitude of x(n).
2. Upsample x(n) byafactor of 2, and plot the DTFT magnitude of the resulting
sequence.
3. Upsample x(n) byafactor of 3, and plot the DTFT magnitude of the resulting
sequence.
4. Upsample x(n) byafactor of 4, and plot the DTFT magnitude of the resulting
sequence.
5. Comment on your results.
P9.14 Using the function interp, study the operation of factor-of-4 interpolation on the
sequences of Problem P9.12. Use the stem function to plot the original and the
interpolated sequences. Experiment, using the filter length parameter values equal to 3
and 5. Comment on any differences in performance of the interpolation.
P9.15 Provide the frequency response plots of the lowpass filters used in the interpolators of
Problem P9.14.
P9.16 Repeat Problem P9.14, using the factor-of-3 interpolation.
P9.17 Provide the frequency response plots of the lowpass filters used in the interpolators of
Problem P9.16.
P9.18 Repeat Problem P9.14, using the factor-of-5 interpolation.
P9.19 Provide the frequency response plots of the lowpass filters used in the interpolators of
Problem P9.18.
P9.20 Using the fir2 function generate a 91-length sequence x(n) whose frequency-domain
sampled values are 0 at ω =0,0.5 at ω =0.1π, 1atω =0.2, 1atω =0.7π, 0.5 at
ω =0.75π, 0atω =0.8π, and0atω = π.
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