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10/2/22, 10:02 PM Submit Lab 4 | Gradescope https://www

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10/2/22, 10:02 PM Submit Lab 4 | Gradescope
https://www.gradescope.com/courses/417083/assignments/2308509/submissions/new 1/5
0/7 Questions Answered
Lab 4
Q1 Bases for N-Dimensional Vectors
10 Points
Assume we consider all audio(n) signals of length , use to
define a basis for . How do you write this basis in matrix form?
Define this matrix as in script1.m in Matlab.
Submit both your explanation and your code here.
Explanation:
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Matlab Code Snippet:
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Q2 Standard Basis for N-Dimensional Vectors
5 Points
Find the representation of audio(n) in terms of the standard basis
(the Identity matrix, with dimension ). In other words, if is our
N δ(n)
RN
A
N × N b
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audio signal, and is our standard basis for , what is if we have
?
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Q3 DCT Matrix as a Basis
15 Points
In the section provided in script1.m , generate the DCT matrix
of size using dctmtx() . Next, write code to prove that is a
basis for . Finally, write out your justification for your procedure.
Submit both your justification and your code here.
Explanation:
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Matlab Code Snippet:
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Q4 DCT Vectors as Elementary Audio Signals
20 Points
A RN x
Ax = b
ADCT
N ADCT
RN
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The DCT vectors can be viewed as elementary audio signals, each
representing some elementary audio frequency. They are ordered by
frequency, with the first column in the matrix corresponding to
the lowest frequency. Write code to play back each of the basis
vectors to show that they lead to increasing frequency.
Submit your code here.
Matlab Code Snippet:
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Q5 Representing Signals in Terms of a New
Basis
20 Points
We are given a signal audio(n) : find its representation in terms of the
DCT basis (the columns of ) by formulating and solving a linear
system of equations.
Submit your code here.
Matlab Code Snippet:
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Q6 Audio Processing
25 Points
ADCT
ADCT
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Design an audio processor that removes the higher frequencies from
audio and plays it back. For example, since the given audio signal
has length you could remove the largest
frequencies. Next, repeat the experiment by removing the lowest
frequencies. Provide code for both versions of this experiment.
Describe your findings by listening to the processed audio signal with
different amounts of low or high frequencies removed (in other words,
change and repeat for each of the two versions of the experiment).
Compare your results between removing the low or the high
frequency vectors.
Submit both your observations and your code here.
Explanation:
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Matlab Code Snippet:
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Q7 Code Submission
5 Points
Submit your completed script1.m code here. Please make sure
you've answered each question in the appropriate section and used
meaningful variable names and comments to help us understand what
you did.
Please select file(s) Select file(s)
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N = 2000 K = 1000
K
K
?
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