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EEL 3135 – Lab #10 solution

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EEL 3135 – Lab #10
Question #1: (Designing a Filter)
There is (somewhat) no Question #1 this week (you do not have to submit anything)! Instead,
we have included a demonstration on how you can design and apply your own filter. The demo
isolates a single note from a clip of xylophone audio. There is also a new function in the comment
code and skeleton code, pz2ba, which you can use to convert pole and zero locations into filter
coefficients b and a. This should help you in the lab.

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Full Name:
EEL 3135 – Lab #10
Question #1: (Designing a Filter)
There is (somewhat) no Question #1 this week (you do not have to submit anything)! Instead,
we have included a demonstration on how you can design and apply your own filter. The demo
isolates a single note from a clip of xylophone audio. There is also a new function in the comment
code and skeleton code, pz2ba, which you can use to convert pole and zero locations into filter
coefficients b and a. This should help you in the lab.
Question #2: (Thinking in Three Domains 1)
The next two problems represent the culmination of the past three z-transform weeks. We want
you to design and implement filters with little additional guidance from us (excluding what is in
eel3135_lab10_comment). Use your knowledge about filters in the time-domain, frequencydomain, and pole-zero space to design appropriate filter systems.
Included with the lab is an audio file “music.wav.” Listen to the audio and you should hear three
instruments: a bass, a mandolin (guitar-like string instrument), and a trumpet. Use MATLAB to
design a filter that retains the bass and removes the mandolin and the trumpet.
Hint: The bass has to lowest frequency, the trumpet has the highest frequencies, and
the mandolin frequencies are in-between..
(a) Answer in your comments: What type of filter did you design: low-pass, high-pass,
band-pass, band-stop, all-pass? Why?
(b) Answer in your comments: Did you create an FIR or IIR filter? Why?
(c) Plot the frequency-domain magnitudes and the time-domains for the input and output signals
(|X(ω)| and |Y (ω)|) (use Question #1 as guidance).
(d) Answer in your comments: What do these plots tell should you about your filter?
(e) Plot the filter impulse response h[n].
(f) Answer in your comments: What does the impulse response tell you about your filter?
(g) Plot the filter magnitude response |H(w)|.
(h) Answer in your comments: What does the frequency response tell you about your filter?
(i) Plot the pole-zero plot of your filter.
(j) Answer in your comments: What does the pole-zero plot tell you about your filter?
(k) Submit your filtered data as a .wav file.
1
Question #3: (Thinking in Three Domains 2)
Included with the lab is an audio file “music.wav.” Listen to the audio and you should hear three
instruments: a bass, a mandolin (guitar-like string instrument), and a trumpet. Use MATLAB to
design a filter that retains the mandolin only (Note: you may not be able to entirely remove the
other instruments entire since there is a little bit of overlap in frequencies – do the best you can).
Hint 1: The mandolin’s frequency band is centered around approximately 505 Hz.
Hint 2: Remember that the normalized frequency ωb = π maps to f = fs/2 in conventional frequency, where fs is the sampling rate.
(a) Answer in your comments: What type of filter did you design: low-pass, high-pass,
band-pass, band-stop, all-pass? Why?
(b) Answer in your comments: Did you create an FIR or IIR filter? Why?
(c) Plot the frequency-domain magnitudes and the time-domains for the input and output signals
(|X(ω)| and |Y (ω)|) (use Question #1 as guidance).
(d) Answer in your comments: What do these plots tell should you about your filter?
(e) Plot the filter impulse response h[n].
(f) Answer in your comments: What does the impulse response tell you about your filter?
(g) Plot the filter magnitude response |H(w)|.
(h) Answer in your comments: What does the frequency response tell you about your filter?
(i) Plot the pole-zero plot of your filter.
(j) Answer in your comments: What does the pole-zero plot tell you about your filter?
(k) Submit your filtered data as a .wav file.
2