Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Some Characteristics of Early Color Vision
The basic material for this discussion is chapter 4 of Brian Wandell's Foundations of Vision,
which will be handed out in class. This page is just a brief ou
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
INTRODUCING THE ZTRANSFORM
After reading this section, you may want to look at Chapter 1, "Signal Processing Basics," in the
User's Guide for the Matlab Signal Processing Toolbox. There are a few thi
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
DFT
FFT
WaveletTransformation
(ext. sources: nbtwiki.net)
including:
5 MATLAB examples
BIOSIGNALVERARBEITUNG
VO 6
%
%
%
%
The frequency in Hz.
The length of the wave in seconds.
Sampling frequency of
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Definition: Biosignal
Many measurement systems for biosignals are low cost and easy to
apply.
Biosignals:
 direct information about its source/sources
 can be acquired often in a noninvasive way

Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
BIOSIGNALVERARBEITUNG
can be represented by a ascending series of closed
Space
is built up by a set of orthogonal wavelets
Both index conventions are equivalent!
There exist other representations with
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
BIOSIGNALVERARBEITUNG
SS 2016
Overview
Analysis (MSA)
Fast Wavelet Transformation based on Multiscale
Discrete Wavelet Transformation (1D DWT)
coefficients
Continuous Wavelet Transformation with disc
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
format short
format compact
echo on
% A.1 Having saved audio1.mat in an accessible folder, we load it:
% MATLAB version:
% load('audio1');
% octave version:
load force 'audio1.mat'
% A.2 Now we plo
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
C IS 558 / Linguistics 525
C omputer Analysis and Modeling of Biological Signals and Systems
Homework 2
The MATLAB fft function implements the Discrete Fourier Transform given by the equation
where N
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
C IS 558 / Linguistics 525
C omputer Analysis and Modeling of Biological Signals and Systems
Homework 3
Due: 2/14/2003
Linear ShiftInvariant Systems
1. (Oppenheim and Shafer 1989 p. 68). The system T
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
The DFT and the FFT
Calculating the DFT
The equations for the DFT (Discrete Fourier Transform) and inverse DFT, using Matlabstyle
indices, are given below:
Discrete Fourier Transform
(Matlabstyle in
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Causal Moving Average (FIR) Filters
We've discussed systems in which each sample of the output is a weighted sum of (certain of
the) the samples of the input.
Let's take a causal "weighted sum" system
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Towards the Discrete Fourier Transform
We spent some time earlier on the first slogan of signal processing:
The response of a linear shiftinvariant system S to an arbitrary input x is the
convolution
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
2. If the color matching matrix for primaries Palt is called Malt, then that the equivalent spectrum
to any 'light' for Palt would be
Palt*Malt*light
This result is another (31element) sampled spectr
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
format compact
format short
echo on
clc
% Generate a complex exponential spiral
% Start with a point on the unit circle
a = pi/4;
z = cos(a) + i*sin(a);
pause
% Move it in a bit
z = .99*z;
pause
% Mak
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Impulse Response and Convolution
Digital signal processing is applied linear algebra? This is easy to grasp for color matching,
where we have fixed dimensions of 1 (number of test lights), 3 (number o
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Linear Algebra Review
Linear Algebra has become as basic and as applicable as calculus, and fortunately it is easier.
Gilbert Strang
Most of digital signal processing can be seen as applied linear al
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
C IS 558 / Linguistics 525
C omputer Analysis and Modeling of Biological Signals and Systems
Homework 1
D ue: 2/1/2005
Things to learn:
Arithmetic on scalars, vectors and matrices; for loops; simple u
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
format short
format compact
echo on
% A.1 Having saved audio1.mat in an accessible folder, we load it:
% MATLAB version:
load('audio1');
% octave version:
% load force 'audio1.mat'
% A.2 Now we plo
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
C IS 558 / Linguistics 525
C omputer Analysis and Modeling of Biological Signals and Systems
Homework 2
Due: 2/15/2005
Color Matching
The background for this homework is the lecture on early color vis
Computer Analysis and Modeling of Biological Signals and Systems
LING 525

Spring 2005
Short time Fourier Transform (STFT)
Gabor transformation
Analysis of nonstationary signals
Windowing and noise
Different window types / effects on signal
In time / frequency domain
Windowing
Topics: