ECE-GY 6113 : DSP 1 Spring 2024
Take Home Exam (Matlab)
Sign and submit the attached oath along with your solutions.
You may use the course resources (lecture videos, demo programs,
assignments, etc) and your own prior work for this course.
You may ask me (Ivan Selesnick) if you have questions about the exam. But you
may not discuss the exam with anyone else. You may not give or get help from
anyone. You may not ask anyone for assistance. Your submitted work must be
100% your own. You may not use any AI tools.
You may consult the web for information (e.g., Matlab documentation) but not to
seek assistance to solve the problems below.
A violation may lead to failing the course.
If in doubt, ask Ivan Selesnick by email at selesi@nyu.edu
1) Notch filtering
For HW 5 Part D, you designed a 4th order notch filter with a second-order notch
to remove tonal noise from a noisy speech signal. Revisit this exercise, but this
time, use the Matlab function butter() to design a Butterworth bandstop filter for
the same purpose. Use the same noisy signal in the exercise.
> Are you able to fully remove the tonal noise from the signal while otherwise
preserving the signal?
> Plot the frequency response, pole/zero diagram, and impulse response of your
Butterworth bandstop filter.
> Compare your Butterworth bandstop filter with the notch filter you designed in
HW 5 Part D. What are the differences and similarities? Comment on how well
the Butterworth bandstop filter functions as a notch filter.
To submit
> Matlab code to reproduce your result.
> audio file in the .wav format of your result.
> Submit a single pdf file containing your plots and discussion.
2) Inverting a system
A speech signal x is distorted by a an LTI system H, implemented in Matlab as follows:
q = [0.4 0.5 -0.3];
L = 300;
b = [q(1) zeros(1, L-1) q(2) zeros(1, L-1) q(3)];
a = 1;
y = filter(b, a, x);
The output signal y is in the file clip2.mp3.
Your task is to recover the signal x. Derive a stable inverse system G. In Matlab,
use your inverse system to recover the signal x. For full credit, implement your
filter using the Matlab filter() function. You might need to use the function more
than once.
To submit
> Matlab code to reproduce your result.
> mp3 file of your result.
> Submit a single pdf file containing:
- your derivation of the inverse system.
- plot of the impulse response h.
- plot of the impulse response g.
- plot of the convolution of h and g.