ECED 4502 Digital Signal
Processing
Jacek Ilow
Dalhousie University
Lecture 1
1
Summary of Lecture
Introduction
Concepts
Analog/Digital
Systems
Digital vs. Analog processing
Hot applications and recent developments
Basic operations on sequences
Basic sequences
Lecture 1
2
Introduction
Discrete:
– Only takes discrete values (as opposed to
continuous)
Time
– The independent variable
– Could be other than time (e.g., space), but we
will use the word time to mean the independent
variable
Lecture 1
3
Introduction ...
Signal
– A function that conveys information
– Domain: One or more independent variables
We
will look at signals with discrete domains
This means that the signal is only defined on those
discrete points
– Amplitude of signal
Can
be either discrete or continuous
Lecture 1
4
Introduction ...
Processing
– We will look at systems which take in a signal
as input and produce another signal as output
– Systems can also be classified in the same way
as the signals
Continuous
time systems
Discrete time systems
Lecture 1
5
Concepts
Continuous
time signals: f(t) defined for all
values of t, where t is a continuous variable
Discrete time signal: fn=f(n) defined only
for discrete (e.g., integral) values of n
Sequences: Representation of a discretetime signal as a sequence of numbers, fn
Lecture 1
6
Concepts...
Digital
signal: both domain (time) and
amplitude of signal are discrete
Analog signal: continuous in both time and
value
Lecture 1
7
Analog/digital systems
Analog signal
Digital signal
Discrete signal
Analog
SP
A/D converter
QuantizSampler
er
Fs≥ 2.Fmax Error is
Analog signal
introduced
-voltage
-speech
-pressure
or
-tape
data from -simulations
-digital devices
DSP
D/A
Digital Signal Processor
-digital computer
-dedicated dig. hw
-programmable hw
Digital signal
Lecture 1
8
Issues
Reconstruction
accuracy
– Conditions for perfect reconstruction
Digital
signal is not just an approx.
representation of an analog signal
– Could be generated digitally
– The processing being performed may not be
realizable in analog
The
theory of discrete time signal
processing is independent of continuous
Lecture 1
9
Digital vs. analog processing
DSP
implementations are flexible,
programmable and modular
More precise and repeatable
Performance and cost effectiveness (riding
the microelectronics wave)
Direct mapping of mathematical
expressions with less approximation
possible (enables sophisticated algorithms)
Lecture 1
10
Digital vs. analog ...
Digital
hardware can be multiplexed better
than analog. Allows integration of multiple
operations and services on a h/w platform
Digital storage is more reliable, cheaper and
more compact
Lecture 1
11
On the other hand
Analog
SP still offers higher bandwidth
Higher dynamic range
Can be very low power
Lecture 1
12
Hot application in DSP
Entertainment:
– digital audio
– digital TV
– multimedia
voice
mail, video and audio conferencing
Medical
imaging/ data analysis
Information services, databases
Meteorology
Lecture 1
13
Hot apps...
Non-destructive
testing of materials
Digital process control for manufacturing
Automotive electronics
Sensor data transmission, storage,
reconstruction
Voice and image synthesis
Environmental monitoring
Lecture 1
14
Developments in DSP
DVD
– CD-ROM size
– Order of magnitude higher data storage
– Same disk can store movies, audio, or data
Very
low bit-rate audio coding
– Internet telephones
Scalable
from
video coding
a few Kbps to several Mbps
Lecture 1
15
Basic operations on sequences
Multiply
two× sequences
z=x.y is defined as z[n] = x[n].y[n]
Add
two sequences
z =x.y is defined as z[n] = x[n]+y[n]
Multiply
a sequence by a constant
z=αx is defined as z[n] = αx[n]
Shifting
by n0
z[n] = x[n−n0]
Lecture 1
16
Basic sequences
Unit
sample sequence
δ[n]=
0,
1,
{
n≠0
n=0
1
0
Lecture 1
17
Basic sequences...
Unit
step sequence
u[n]=
0,
1,
{
n<0
n≥0
1
0
Lecture 1
18
Basic sequences...
Sinusoidal
sequence
x[n]=Αcos(ω0 n+φ)
0
Lecture 1
19
Basic sequences...
Exponential
sequence
0<α<1
x[n]=Aαn,
A
0
x[n]=Aαn,
α>1
A
0
Lecture 1
20
Exponential sequence
If
α and A are complex
α = |α|ejωo and A= |A|ejφ
x[n] = Aαn = |A|ejφ|α|nejωon
= |A||α|nej(ωon+φ)
= |A||α|ncos(ωon+φ) + j|A||α|nsin(ωon+φ)
ωo
is called the frequency, φ the phase
Lecture 1
21
Sinusoids and exponentials
A signal with frequency ωo+2πk is identical to
one with frequency ωo
Exponential
signal
– Ae j(ωo+2πk) n = Ae jωone j2πkn = Ae jωon
Sinusoidal
– Acos((ωo+2πk)n+φ) = Acos(ωon+φ)
We
only need to consider an interval of
length 2π (e.g.,−π< ωo≤ π or 0≤ωo<2π)
This is not true for continuous time signals
Lecture 1
22