We would like to design a bandpass filter in a DSP system which attenuates a signal outside the range of frequencies from 1000 Hz to 2000 Hz with near unity gain within the passband. The maximum bandwidth for any input signal is below 5000 Hz. (a) What is the minimum sampling rate f, that should be used for this DSP system? (b) With a sampling rate equal to fs, start by designing a corresponding lowpass filter, using a rectangular window of length 60. Note that you will afterwards transform this lowpass filter into the required bandpass filter, so choose the parameters accordingly. Write the expression for the impulse response hLP[n] of this filter. (c) Find the impulse response hep[n] of the bandpass filter by transforming the appropriate lowpass filter from part (b). Note: Be careful when applying equations from Slide 20.11. The derivation on Slide 20.11 assumed no "delay" to make the filter causal. If your resulting hap[n] is not symmetric, then you have not applied the delay appropriately. (d) Using MATLAB, plot the magnitude of the frequency response of the resulting bandpass filter. (e) Now design the same filter, but use a von Hann window instead of a rectangular window. Using MATLAB, plot the magnitude of the frequency response of this bandpass filter and compare it to part (d).
We would like to design a bandpass filter in a DSP system which attenuates a signal outside the range of frequencies from 1000 Hz to 2000 Hz with near unity gain within the passband. The maximum bandwidth for any input signal is below 5000 Hz. (a) What is the minimum sampling rate f, that should be used for this DSP system? (b) With a sampling rate equal to fs, start by designing a corresponding lowpass filter, using a rectangular window of length 60. Note that you will afterwards transform this lowpass filter into the required bandpass filter, so choose the parameters accordingly. Write the expression for the impulse response hLP[n] of this filter. (c) Find the impulse response hep[n] of the bandpass filter by transforming the appropriate lowpass filter from part (b). Note: Be careful when applying equations from Slide 20.11. The derivation on Slide 20.11 assumed no "delay" to make the filter causal. If your resulting hap[n] is not symmetric, then you have not applied the delay appropriately. (d) Using MATLAB, plot the magnitude of the frequency response of the resulting bandpass filter. (e) Now design the same filter, but use a von Hann window instead of a rectangular window. Using MATLAB, plot the magnitude of the frequency response of this bandpass filter and compare it to part (d).
Chapter8: Data And Network Communication Technology
Section: Chapter Questions
Problem 2PE
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![We would like to design a bandpass filter in a DSP system which attenuates a signal outside the
range of frequencies from 1000 Hz to 2000 Hz with near unity gain within the passband. The
maximum bandwidth for any input signal is below 5000 Hz.
(a) What is the minimum sampling rate f, that should be used for this DSP system?
(b) With a sampling rate equal to fs, start by designing a corresponding lowpass filter, using a
rectangular window of length 60. Note that you will afterwards transform this lowpass filter
into the required bandpass filter, so choose the parameters accordingly. Write the expression
for the impulse response hLP[n] of this filter.
(c) Find the impulse response hep[n] of the bandpass filter by transforming the appropriate
lowpass filter from part (b).
Note: Be careful when applying equations from Slide 20.11. The derivation on Slide 20.11
assumed no "delay" to make the filter causal. If your resulting hap[n] is not symmetric, then
you have not applied the delay appropriately.
(d) Using MATLAB, plot the magnitude of the frequency response of the resulting bandpass filter.
(e) Now design the same filter, but use a von Hann window instead of a rectangular window.
Using MATLAB, plot the magnitude of the frequency response of this bandpass filter and
compare it to part (d).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcbe86c78-5399-4e86-a38b-6159fa30d2d1%2Fcccd7811-8413-47b4-9d88-730e30d76617%2F97169k_processed.png&w=3840&q=75)
Transcribed Image Text:We would like to design a bandpass filter in a DSP system which attenuates a signal outside the
range of frequencies from 1000 Hz to 2000 Hz with near unity gain within the passband. The
maximum bandwidth for any input signal is below 5000 Hz.
(a) What is the minimum sampling rate f, that should be used for this DSP system?
(b) With a sampling rate equal to fs, start by designing a corresponding lowpass filter, using a
rectangular window of length 60. Note that you will afterwards transform this lowpass filter
into the required bandpass filter, so choose the parameters accordingly. Write the expression
for the impulse response hLP[n] of this filter.
(c) Find the impulse response hep[n] of the bandpass filter by transforming the appropriate
lowpass filter from part (b).
Note: Be careful when applying equations from Slide 20.11. The derivation on Slide 20.11
assumed no "delay" to make the filter causal. If your resulting hap[n] is not symmetric, then
you have not applied the delay appropriately.
(d) Using MATLAB, plot the magnitude of the frequency response of the resulting bandpass filter.
(e) Now design the same filter, but use a von Hann window instead of a rectangular window.
Using MATLAB, plot the magnitude of the frequency response of this bandpass filter and
compare it to part (d).
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