ECE-2026 Lab #3 Spring-2023
LAB COMPLETION REPORT
Name: Ivan Mix, Carl Cort, Christian Choi, Adnan Porbanderwala
Part 3.1 Chirp Aliasing
(a) Chirp formula: cos(ψ(t)) = cos⁡(2𝜋µ𝑡 2 + 2𝜋𝑓0 + 𝜑)
= 𝒄𝐨𝐬⁡(𝟐𝝅(𝟕𝟓𝟎𝒕𝟐 + 𝟔𝟐𝟓 + 𝒓𝒂𝒏𝒅𝒐𝒎)
(b) LSECT = 128 samples and TSECT = 0.0512 sec
(c) Guess why there are “ups and downs” in spectrogram (more about sampling and aliasing in
Lab #4):
The “ups and downs” are caused by aliasing. More specifically, the negative sloped parts are the
folded sections (like the time segment between fs/2 and fs) while the positive sloped sections
other than the first positive sloped part at the beginning of the graph are simple aliasing. Then it
alternates back and forth between folding and simple aliasing.
Code:
%% 3.1
clc; clear; close all
fSamp = 2500 %-Number of time samples per second
dt = 1/fSamp;
tStart = 0;
tStop = 5;
tt = tStart:dt:tStop;
mu = (8125 - 625)/(tStop - tStart)*0.5
fzero = 625;
phi = 2*pi*rand; %-- random phase
Lsect = 128;
Tsect = Lsect*dt
%
psi = 2*pi*mu*tt.*tt + 2*pi*fzero*tt + phi;
%% <=================== FILL
IN THE CODE HERE %
cc = real( exp(j*psi) );
%soundsc( cc, fSamp ); %-- uncomment to hear the sound
plotspec( cc+j*1e-12, fSamp, Lsect ), colorbar, grid on %-- with negative
frequencies
xlabel("sec")
ylabel("Hz")
% I messed around with it and if you sample at a higher frequency it
sounds
% and looks like a simple chirp signal instead of having aliasing issues
Part 3.2 Spectrogram of periodic full-wave rectified sine wave using a long section duration.
(b) TSECT = 1 sec and LSECT = 5000 samples
(d) List frequencies of visible harmonics = I can see horizontal lines (frequencies) at +-0, +-2,
+-4, +-6, +-8 (Hz)... there are probably very faint ones at +-10Hz, and so on (2kHz where k is an
integer), I just can't see them because they are too faint or the Tsect is not long enough to have
that resolution
(e) Fundamental Frequency = they are at every 2n, therefore fundamental is 2Hz
(f) |a1|= -0.2122 |a3|= -0.0182 and dB difference = abs(20*(log10(a3) - log10(a1)))
= 20*(log10(a1/a3)) = 21.3389Db
Code:
%% 3.2
clc;clear;close all
%% Fill in the values
fs = 1000;
Amp = 1;
T = 1; %period
tStop = 5;
tt=0:(1/fs):tStop;
xx=Amp*abs(sin(2*pi*tt/T));
Tsect = 5;
Lsect = Tsect*fs
figure
plot(tt,xx);
title('Full-wave Rectified Sine'); xlabel('t [sec]')
figure
plotspec( xx+j*1e-12, fs, Lsect ), colorbar, grid on %-- with negative
frequencies
ylabel("Hz")
xlabel("sec")
% *****Hint: Zoom in on the verticle axis to see the harmonics*****
% Fundamental freq = ???
%% GUI
fseriesdemo
%<==Uncomment to use the GUI
%I can see horizontal lines (frequencies) at 0, 2, 4, 6, 8 (Hz)... there
is
%probably a very faint one at 10 and so on, I just can't see it
% a1= - 2/(3*pi)
% a3= - 2/(35*pi)
% (e) since there are lines every 2, gcd is 2, fundamental frequency = 2Hz
% 1st mag = .212
3rd mag = 0.018
Part 3.3 Questions about decibels:
(a) Explain 6 dB. A 6 decibel difference means the amplitude is twice as large, because if you
look at something that is not in decibels and compute the difference, logarithm properties allow
you to combine the difference into a single logarithm of the ratio of the two. If the first one is
twice the other, this will be log10(2), which is about 0.3, and when you multiply by 20
(20log10(x) is its value in decibels) that will be 6Db.
(b) dB difference between |a1|and |a3| = 21.3389Db (from 3.2f)… this is again because the
decibel value of the first one minus the second one can be found by
= 20log10(a1) – 20log10(a3) = 20(log10(a1) – log10(a3)) = 20log10(a1/a3)… and a1/a3 = 35/3
which gives 20log10(a1/a3) = 20 * 1.0669 = 21.3389Db
Code:
%% 3.3
clc;clear;close all
a1 = - 2/(3*pi)
a3 = - 2/(35*pi)
dB_difference = abs(20* (log10(a3) - log10(a1)) )
Part 3.4 dB-Spectrogram of periodic full-wave rectified sine wave using a long-duration section.
(a) List frequencies of harmonic lines = for part (a) there are lines every 2kHz where k is an
integer and for part (b) there are lines every kHz where k is an integer.
(b) Best value of TSECT = 4 seconds
Zoomed in images of the decibel color-scaled plots of the two rectified sin waves spectrograms.
The plot on the left is the fully rectified sin wave with one second period and on the one on the
right is the one with a 2 second period. Below it are the plots not zoomed in as much.
Code:
%% 3.2
clc;clear;close all
%% Part(a)
fs = 1000;
Fill in the values
Amp = 1;
T = 1;
tStop = 5;
tt=0:(1/fs):tStop;
xx=Amp*abs(sin(2*pi*tt/T));
Tsect = 5;
Lsect = Tsect*fs;
DBrange = 10000;
figure
plotspecDB( xx+j*1e-12, fs, Lsect, DBrange), colorbar, grid on %-- with
negative frequencies
ylabel("Hz")
xlabel("sec")
%% Part(b)
fs = 1000;
Amp = 1;
T = 2;
tStop = 5;
Fill in the values
tt=0:(1/fs):tStop;
xx2=Amp*abs(sin(2*pi*tt/T));
Tsect = 4;
Lsect = Tsect*fs;
DBrange = 10000; %decimal val of 80dB = 10^(80/20)
figure
plotspecDB( xx2 + j*1e-12, fs, Lsect, DBrange), colorbar, grid on %-- with
negative frequencies
ylabel("Hz")
xlabel("sec")
Part 3.5 Using the voice signal that you have recorded for Lab #1, make a linear and a dB
spectrogram with a long section length, e.g., LSECT = 512. Since the vowel region of the
recording is a signal that is quasi-periodic, the spectrograms should exhibit a harmonic line
characteristic (parallel horizontal lines) during that time. Try different section lengths LSECT
until the harmonic lines are easy to see in the spectrograms.
Tried several LSECTs and found that 440 samples was the best LSECT for overall clarity. Using
this LSECT, the spectrogram plots look like this (regular color scaling on the left and Db color
scaling on the right:
Based on the plots, within the vowel region (the set of roughly harmonic lines around 0.4secs)
there are frequency lines at about ~130, 260, 400, 540 Hz. Based on this, it looks like the
fundamental frequency is about 130Hz.
Code:
%% 3.5
clc; clear; close all
[xx,fs] = audioread('ece2026lab1.wav');
Tsect = 0.055;
Lsect = Tsect*fs
DBrange = 80;
% Linear spectrogram
figure
plotspec( xx, fs, Lsect), colorbar, grid on %-- with negative frequencies
ylabel("Hz")
xlabel("sec")
% DB spectrogram
figure
plotspecDB( xx, fs, Lsect, 10^(DBrange/20)), colorbar, grid on %-- with
negative frequencies
ylabel("Hz") %Scale is still Hz but color grading is in decibells
xlabel("sec")