Homework1 LTI systems, FT of DT signals
1. Determine whether the system has the following properties: stability, causality, linearity,
time-invariance, memorylessness. Present your reasoning!
T (x[n]) = a x[n]
T (x[n]) = z [n] x[n], z [n] = (1)n
T (x[n])

EDISP (Filters intro )
(English) Digital Signal Processing
Digital/Discrete Time/ lters introduction
lecture
November 26, 2007
DT system characteristics
An LTI system is described with its impulse response
x [n]
y [n]
h(k )
y (n ) =
h(k ) x (n k )
k =
but

EDISP (Filters 2)
(English) Digital Signal Processing
Digital (Discrete Time) lters 2
lecture
December 10, 2007
How an LTI system lters signals
A practical system and its difference equation
Difference equation and H (z )
Short path: system H (z )
System

Test 2 (2007/8) version B inst. spectrum, z -transform, lters
Please mark your name and test version on all your answer pages
1. (3 p.) The instantaneous spectrum X (ej , n) of a signal
x(n) =
1
0
for M/2 n M/2
otherwise
(Assume M is even)
is computed usi

EDISP 2008/2009 Final exam0, version A 27.01.2009
1
2
3
4
5
Name:
Solve long problems on an additional sheet,
marked with your name. For the short problems, try to write the answer in the provided
space. Put your calculations on the additional
sheet.
1. (

EDISP 2008/2009 Final exam0, version B 27.01.2009
1
2
3
4
5
Name:
Solve long problems on an additional sheet,
marked with your name. For the short problems, try to write the answer in the provided
space. Put your calculations on the additional
sheet.
1. (

I used MATLAB too!
1
Lesson [10]
Windowing
Windowing
Whats it all about?
Challenge 09
Windows
Challenge 10
Project
Exam #1 ave. 90
2
Lesson [10]
Challenge 09
DTMF, or dual tone multi-frequency modulation, associates two tones with each
key on a touch-tone

1
Lesson [11]
Cooley-Tukey FFT
Challenge 10
Cooley-Tukey FFT
Derivative FFT forms
Challenge 11
2
Lesson [11]
Challenge 10
Windows are multiplicative appliques that cosmetically make a signal to
appear to be more periodic than it is thereby mitigating (som

EDISP (Z-transform )
(English) Digital Signal Processing
Z-Transform lecture
November 19, 2007
z -transform
Z a generalization of DTFT, similar to L as a generalization of CTFT
X (z ) =
x (n)z n
n=
DTFT is equal to X (z ) at unit circle z = ej
Convergen

EDISP (Inst. Spectrum - STFT )
(English) Digital Signal Processing
Instantaneous spectrum
or
Short Time Fourier Transform lecture
November 2, 2009
Signal properties changing in time
FT/DFT etc: signal properties assumed constant in a whole analysis
time
T

Homework2/0809+ z-transform, inst. spectrum, lters
1. The instantaneous spectrum X (ej , n) of a signal
x(n) =
z (n)
0
for n = 10, . . . , 49
otherwise
is computed using rectangular window g (k ) of length K = 10.
Assume i) z (n) = 1 ii) z (n) = ej0 n iii

EDISP (L jpeg) January 21, 2008
1
Compression of signals
Split into blocks (frames)
Use suitable transform to condense information
Signal model
Perception model
Remove some information (for lossy compression)
Match channel capacity
Apply human perc

A
EDISP (L9) Revision : 1.5 LTEXed on January 8, 2008
1
Randomness
We describe as random effects that are too complex to precisely analyze in practice, or
simply unknown:
physical noise: thermal, mechanical, acoustic, radio/radar
somebodys decisions mad

EDISP (NWL2)
(English) Digital Signal Processing
Transform, FT, DFT
October 13, 2011
Transform concept
We want to analyze the signal represent it as built of some buliding
blocks (well known signals), possibly scaled
x [n] =
Ak k [n]
k
The number k of bl

EDISP (NWL3)
(English) Digital Signal Processing
DFT Windowing, FFT
October 24, 2011
DFT resolution
N-point DFT frequency sampled at k = 2Nk , so the resolution is
fs /N
If we want more, we use N1 > N lling with zeros (zero-padding)
but IDFT will give N1

EDISP (FFT)
(English) Digital Signal Processing
FFT lecture
November 5, 2007
Fast DFT algorithms FFT
Direct computation with pre-computed WN = ej 2/N (twiddle factors) :
N 1
X e j k
=
kn
x (n)WN
n=0
complexity: N 2
Goertzel algorithm: X (k ) = yk (N ), w

EDISP (Win + FFT app )
(English) Digital Signal Processing
Windowing and FFT applications lecture
November 6, 2007
Limited observation time
For DFT we used to cut a fragment of the signal
x0 [n] = x [n]g [n], where g [n] =
1
0
for
for
n = 0, 1, . . . , N

1Course Number & Name: EEL 4310 and EEL5322 - Digital Integrated Circuits Design
Credits and Contact Hours: 3 crs; 3 classes per week of 50 minutes each
Instructors or Course Coordinators Name: Dr. Scott E. Thompson
Contact info
Prof. Scott Thompson
535 E