Homework # 2
EE331 Signals & Systems 2011 Fall IYTE
Deadline: October 17, 2011, 10:30 AM
Q.1. Express each of the following complex numbers in Cartesian form (x +jy):
a) (1/2) e - j , b) 2 e - j/4
Q.2. Express each of the following complex numbers in pola
Fourier Transform/Series
Representation of Signals and Systems
Fourier Series representation of periodic continuoustime signals
Fourier Transform representation of aperiodic
continuous-time signals
Properties of Fourier Transform
Magnitude and phase o
1-D FOURIER TRANSFORMS
Vedat Tavanolu
1-D Fourier Transforms
Continuous-Variable Fourier Transform of a 1-D Signal
X
Fa ( j) f a ( x)e
jx
dx
0
Fourier Transform of Rectangular Fuction
f a (x)
X
Fa ( j) A e
A
x
Vedat Tavanolu
1-D FOURIER TRANSFORMS
jx
dx
EE434 Biomedical Signal Processing Course
Homework # 1
Deadline: February 28th, 2017, 13:30
The electroneurogram (ENG) propagation of nerve action potential
The electromyogram (EMG) electrical activity of the muscle cells
The electrocardiogram (ECG) elect
EE331
Signals & Systems
EE331: Signals and Sytems Canan
Aydodu @ zmir Institute of Technology
1
Introduction to Course
EE331: Signals and Sytems
Canan Aydodu @ zmir Institute of Technology
2
If you are determined to do
engineering
EE331: Signals and Syte
Chapter 2
Brushing Up on Math
In This Chapter
Reviewing basic algebra
Finding the love for trig
Calculating complex arithmetic
Recalling calculus
Rooting for polynomials
C
an you believe it? A mathematics review chapter in a signals and systems book!
FREQUENCY-DOMAIN IMPLICATIONS OF TRUNCATING
OR RECTANGULAR-WINDOWING A SINUSOIDAL SIGNAL
IN THE TIME DOMAIN: THE FREQUENCY LEAKAGE
Consider the sinusoidal signal
x n cos 0 n
2
and N0 is the number of samples in one cycle or the period. Obviously there is
SS-1-2003-BS
2003
SS-1-2003-B-CA2
SS-1-2003-B-CA3
2004 yl arasnavnda gizli grup uygulamas yaplm ve 4 grup halinde sorular sorulmutur. Hepsinin cevaplar
soru kd zerinde olup 5. sorunun zm aklamal olarak ayr bir sayfada yaplmtr. 5. soru tm
gruplarda ayn bii
Motivasyon
Zamandan
bamsz sistem
(LTI)
Saysal aret & Sistemler
Giri
+
H(z)
G(z)
1
3
erik
2
Temeller > Sinyaller
Motivasyon
Ders ierii
Temeller
Bir sinyalin g ve enerji ierii
Zaman deikeninin transformasyonu
ift ve Tek Sinyaller
Geni tanm: Bamsz deikenleri
[CHAP. 1
SIGNALS AND SYSTEMS
(4
Fig. 1-24
1.6.
Find the even and odd components of x ( r )
Let
x,(r)
and
x,(I)
= eJ'.
be the even and odd components of
ei',
respectively.
eJ' = x , ( I ) + x , ( I )
From Eqs. ( 1 . 5 ) and
(1.6)
and using Euler's formula,
IMPULSE SAMPLING
Impulse sampling is of f (t ) is defined by
f* (t ) f (t ) p* (t )
where p* (t ) is the impulse train
p* (t )
with the impulse defined as
(t nT )
s
n
(t ) 0 for t 0
and
(t )dt 1
It follows that
hence
f (t ) (t ) f (0) (t )
f (t ) (t
96
4
The ContinuousTime Fourier Transform
Fourier (or frequency domain) analysis turns out to be a tool of
even greater usefulness
Extension of Fourier series representation to aperiodic signals
Foundation of frequency-domain methods for continuous-time s
EE331
Signals & Systems
EE331: Signals and Sytems Canan
Aydodu @ zmir Institute of Technology
1
Linear System
Linear System: A system is linear if and only if
x1(t)
y1(t)
x2(t)
y2(t)
Linear System
x1(t) + x2(t)
y1(t) + y2(t)
a.x1(t) + b.x2(t)
a.y1(t) + b
EE 331 - Lab HW#2
Quiz Date: October 17, 2016
2
Homework
2.1
Moving Average (MA) Filters
Moving average (MA) operation is a well-known calculation (especially in finance) which is utilized to analyze
the data (time series) trend in a window of time. This
The Laplace Transform
Generalized form of Fourier Transform: s is
not limited to j, can be any complex number An eigen vector:
For any LTI system:
e
st
x(t ) e st
y (t ) x(t ) * h(t )
y (t ) ( ) x(t )d ( )e s (t ) d
h
h
y (t ) e
st
h( )e
s
st
d e H ( s )
LAB 5: Time-domain processing of Signals
Lets load a speech file, play and plot it:
>[s,sampFreq]=wavread(ses.wav)
>soundsc(s,sampFreq);plot(s)
Our first task will be to plot the envelope of the signal on top
of the signal. Then we will perform periodic-a
LAB 3: Edge detection on images
An image is simply a matrix that can be viewed by:
>image(x)
Lena: Celebrity for EEs
Lets load and plot an image:
>load lena.mat
>image(lena)
Lets check the contents of the matrix:
>lena(1:5,1:5)
We can convert the color ma
input sequence, signal, array, .
This is a
continuous-time
system.
Example discrete-time systems
Gecikme
nd=10
M1=2 M2=2
M1=10 M2=10
Akmlatr,toplayc
(Bellekli, Belleksiz)
Time-invariant systems
Zamanda deimezlik
x[n]
Tcfw_.
y[n]
x[n-n0]
Tcfw_.
y[n-n0]
To
Sampling of continuous time signals
DSP systems have several advantages when compared to the CT
systems:
Flexibility due to (re)programmability
Computational accuracy and stability
Easy reproducibility
Efficient implementation: DSP processors and appl
LAB X: Heart-rate detection from
ECG signals
More then two
connections are used to
obtain the signal in a
differential manner.
This helps removal of
common mode
components.
Here is how an ECG signal looks like:
You can load some ECG signals by:
>load ecgS
LAB 2- ZERO CROSSING:
Zero-Crossing: is a commonly used term in electronics,
mathematics, and image processing. In mathematical terms, a "zerocrossing" is a point where the sign of a function changes (e.g. from
positive to negative), represented by a cros
LAB 1: Data Read-Write
Demo Task: Write a function that
creates a random sequence of numbers (an array)
-> size specified by the user
writes it into a text file -> file specified by the
user
Main Task: Write a function that
Reads data from a text file