2021, EEL EEL3135: Exam #
(a) (6 pts) Compute the energy of the signal x[n].
(b) (6 pts) Compute the output of the system
y[n] =
∞∑
k=−∞
Akb x[n−Nbk]
The output should be defined along the provided time axis nx – e.g., the first value of your
output should correspond to the y[n] at n = the first value in nx. Trim your output, if
necessary. Assume all values of x[n] outside the input range nx are zero.
(c) (7 pts) Compute the output of the system
y[n] = x[−n]
The output should defined along the provided time axis nx (trim your output). Assume all
values of x[n] outside the input range nx are zero.
(d) (7 pts) The signal z corresponds to 2000 spoken numbers (feel free to play it – warning, it
is longer than an hour). The recording of each number are provided as .wav files. Identify
how many times the number defined in variable alpha is spoken.
(a) (6 pts) Compute the system output for 0 ≤ n ≤ 100 (i.e., length 101) for input
x[n] = (1/4) (u[n− 6] − u[n− 26]) .
(b) (6 pts) Is the system linear (note: not linear phase)?
(c) (6 pts) Is the system time-invariant?
Question #2: For this question, the function
y2 = exam01_q2(ID, x2);
provides y2, the output of a causal system with input x2. In this problem, assume all signals start
at n = 0. Answer the following questions.
Provided is a template script exam01.m with useful functions. For each question, there is an
associated obfuscated MATLAB function (files with a .p extension):
output = exam01_q#(ID)
where the input UFID should be your ID as a string. Make sure this is correct.
Question #1: For this question, the function
[nx, x1, nz, z1, fs, Ab, Nb, alpha] = exam01_q1(ID);
provides two signals x1 (or x[n]) and z1 (or z[n]) with respective time axes nx and nz and sampling
rate fs (in Hz). It also includes parameters Ab, Nb, and α for the sub-questions below.
(a) (6 pts) Identify if Filter 1 is stable or unstable.
(b) (6 pts) Identify if Filter 1 is linear phase.
(c) (6 pts) Identify if Filter 1 is a low-pass, high-pass, band-pass, band-stop, or all-pass.
(d) (6 pts) Filter 2 is a band-pass filter. Identify the center of its passband as a DTFT frequency
between −π ≤ ω < pi.
(e) (7 pts) Design a set of filter coefficients (i.e., new b and a values) that can emulate Filter 2.
Use only two poles (with two zeros at the origin).
(a) (6 pts) Identify the length of x4a, in seconds.
(b) (6 pts) Identity the Nyquist sampling rate (in Hz) for the data (i.e., the minimal sampling
rate we can apply to the original continuous time signal without aliasing).
(c) (6 pts) A second message x4c contains noise isolated at several different frequencies. Iden-
tify the number of interfering frequencies in our data (count negative and positive frequencies
as separate frequencies – i.e., cos(ω0n) has two frequencies, a positive and a negative).
(d) (7 pts) Now, remove these interfering frequencies from the data. Provide the filter coeffi-
cients (b and a) for a filter that will remove these frequencies.
Question #4: For this question, the function
[x4a, x4c, fs4] = exam01_q4(ID);
outputs two signals x4a and x4c and their associated sampling rate fs4 (in Hz).
Question #3: For this question,
[b3,a3,h3] = exam01_q3(ID);
outputs information about two filters. For Filter 1, the function provides the filter coefficients (b
and a). For Filter 2, the function provides an impulse response h3.
Question #1
Question #2
Question #3
Question #4