Assignment III - Biosignals and Systems EECE 434
Problem 1:
Part I: Distorted speech file
clear all
N = 200;
b = zeros (N, 1);
b(1) = 1;
b(N) = 1.2;
yq = wavread ('EchoSpeech.wav');
player = audioplayer(yq, 8000);
play(player);
a=1;
[hz,hp,ht]=zplane(b',a
Assignment I - Biosignals and Systems EECE 434
Problem 1:
Problem 2:
Problem 3:
Problem 4:
Problem 5:
clear all
close all
R = 50;
d = rand(R,1)-0.5;
m = 0:1:R-1;
s = 2*m.*(0.9.^m);
x = s + d' ;
plot(m,d,'r-',m,s,'b-',m,x,'g:')
xlabel('Time index n'); ylab
EECE 434
Parametric signal models: An
introduction to linear prediction
1
Linear prediction
2
Reminder
n
Let us consider a real wide-sense stationary process cfw_x(n) with
autocorrelation sequence cfw_ xx (m) and power spectral density.
xx ( m ) = Ecfw_
EECE 434
Random signals and processes introduction
Random Variables; PDF
Basic Estimation: Expectation
Random processes:
e.g. white noise process
Mean, auto-correlation function
1
Deterministic signals vs. random
n
n
n
We covered mathematical representati
EECE 434
An introduction to support vector machine classification
Mehdi Moradi, Ph.D., P.Eng.
Electrical and Computer Engineering
University of British Columbia
moradi@ece.ubc.ca
1
1
Support Vector Machines
! A very good reference
! Pattern Recognition an
EECE 434 - Lectures 12
Mehdi Moradi
DFT continued
Symmetry property of DFT
Example: A continuous real valued signal is sampled at 5KHz, then we
calculate DFT with N=512 to get X[k]. We know X[11] = 1+j, what
can be said about X[501]? What physical frequen
Regression and regularization
Mehdi Moradi, Ph.D., P.Eng.
Electrical and Computer Engineering
University of British Columbia
moradi@ece.ubc.ca
1
Most slides from Hastie, et al.
textbook.
1
Regression
Regression: the outcome measurement is cardinal or
quan
EECE 434 - Lecture 11
Mehdi Moradi
Discrete Fourier Transform of a finite duration signal
2
Fourier analysis
DTFT:
(-, )
DFT: k
k=0,1,N-1
=2f/Fs
CFT: f
f(-, )
k=2k/N
Duality:
If a signal is periodic, its Fourier transform is discrete!
The Fourier trans
EECE 434 - Lecture 3
Mehdi Moradi
Basics of discrete -me signals and systems
Common visual presentation of a
discrete time signal as a sequence
where n is an integer. In a prac0cal se2ng, such sequences can o7en arise from periodic
EECE 434 - Lecture 9
Mehdi Moradi
Z transform: A tool for analysis of LTI systems
Properties of z-transform:
Time shifting:
Very useful in calculating the inverse:
1
1
1
=
(]1 [ ) ( = ) > :
1
4
4
4
2
Mehdi Moradi
z-Transform: Properties
Linearity
z
EECE 434 - Lecture 7-8
Mehdi Moradi
Quantization error
The concept of correlation and an introduction to system identification
Z transform: A tool for analysis of LTI systems
Signal Quantization
Quantization: conversion of continuousvalued signal into dis
EECE 434 - Lecture 10
Mehdi Moradi
All pass Minimum phase systems
All pass filters
Each pole comes with its conjugate reciprocal zero
All-pass with complex poles/zeros
Each pole also has to be matched with its conjugate pole (for
the system response to be
EECE 434 - Lecture 2
Mehdi Moradi
Reminder from last week:
Signal: any physical quan0ty that varies with 0me,
space, or any other independent variable or variables
(includes images and video).
Digital: a discrete-0me and dis
EECE 434 - Lecture 6
Mehdi Moradi
Closing the LTI systems
Sampling of continuous time signals
Steady State Response of LTI systems to input sine
and cosine and complex exponential inputs
NOTE: These are time domain equation. We are looking for the respons
EECE 434 - Lecture 4
Mehdi Moradi
Properties of the DTFT
Discrete system theory
Discrete Time Fourier Transform (DTFT)
Spectral analysis is the process of determining the frequency contents of a signal. The
Fourier analysis plays the role of the prism in
EECE 434
Biosignals and Systems
Jan April 2014
Mehdi Moradi, Ph.D.
Electrical and Computer Engineering
University of British Columbia
http:/courses.ece.ubc.ca/434/
1
moradi@ece.ubc.ca
1
Practical Information
The course outline
2
Practical Information
Inst
EECE 434 - Lecture 5
Mehdi Moradi
Discrete systems
The behaviour of LTI systems: transient and steady state response
LTI systems = Linear and Time Invariant
Important feature of LTI systems:
You know the response of the system to the impulse sequence,
yo