digital signal processingnwpu-dsp.com/lecture_notes/1-1 signals.pdf · 2020-01-06 ·...
TRANSCRIPT
Digital Signal Processing
Prof. Dr. WAN Shuai
School of Electronics and Information
Northwestern Polytechnical University
(International Class, 2019)
Dr. WAN Shuai◼ B.E. in Telecommunication Engineering (2001) Xidian University◼ M.E. in Communication and Information System (2004) Xidian University◼ Ph.D. in Electronic Engineering (2007) Queen Mary, University of London
◼ Associate Professor & Supervisor for Master Students (2008)◼ Professor & Supervisor for Doctorial Candidates (2014)
Northwestern Polytechnical University◼ Adjunct Professor (2016) RMIT University, Australia
◼ Research interests: Video technologies◼ Email: [email protected]; Mobile: 13659188123
◼ Office: No. 349, Electronics & Information Building
About this course◼ Provincial Elaborate Course (2012)
◼ Provincial Elaborate Source Sharing Course (2015)
◼ Brand English Teaching Course for Study in China, Ministry of Education of China (2016)
◼ EMI training program at Oxford University (2017)
◼ Internet Classroom (2018)
◼ Textbook:A. V. Oppenheim etc., Discrete-Time Signal Processing (third edition)Website: https://www.pearsonhigered.com/oppenheim
◼ Reference:
a) MIT Open Courseware of Digital Signal Processing:
https://ocw.mit.edu/resources/res-6-008-digital-signal-processing-spring-2011/introduction/
b) Tools for Digital Signal Processing in Matlab:
https://cn.mathworks.com/solutions/dsp/
c) Digital Signal Processing MOOC on Cousera：
https://www.coursera.org/learn/dsp
Final Score◼ Assignment : (10%)◼ Quizzes & Discussions (20%)◼ Examination (70%, Final)
◼ Lab course: (separate 100%)
Course Outline◼ signal and systems
◼ Frequency and transform-domain analysis (Fourier transform, z-transform, discrete Fourier transform, fast Fourier transform…)
◼ Digital processing of analog signals (Sampling, reconstruction, quantization …)
of discrete-time systems
◼ Filter design - (IIR, FIR)
◼ Examples: DSP in life and applications
◼ Lab Course – your realization of DSP
Digital Signal Processing
◼ Signal: Convey information about the state or behavior of a physical system.
◼ Examples:
Voltage, Current, Temperature, Speed…
Different from INFORMATION
Classification of Signals◼ Signals are represented mathematically as functions of one or
more independent variables.
◼ A common convention of the variable: Time
◼ For a signal, both the variable of time and the amplitude can either be continuous or discrete.
Digital Signal or NOT?
上证综合指数SSE Composite
Index新浪财经
http://finance.sina.com.cn/realstock/company/sh000001/nc.shtml
Digital Signal – long history…
Stone TabletFlood in Nile 2500 B.C.
GoetheTemperature
in Yena1820 A.D.
the Great Ultimate, the
Eight Hexagrams, to be determined;I Ching,1000B.C.
Digital Signal Processing◼ Process the signal: analysis, interpretation, and manipulation.
◼ Signal processing has a long and rich history.
◼ Applications
communications, entertainment, military, space exploration, medicine, archaeology…
Everywhere…
Why digital signal processing?
◼ Digital devices: PC, VLSI digital signal processors
◼ Advantages (over analog signal proc.):
Flexible and programmable
Reliable and accurate
Easy to implement by VLSI
Think about A vs D in Mobile, Tape&CD, TV set, Communications…
Finding DSP in the real world…
◼ Telecommunications
Digital Network - DSP
0101000001 0101000001
A/D D/AMore examples of DSP?
Finding DSP in the real world…
◼ Recognize telephone number through the sound of keypad
95588
Discrete-Time Signals: Sequences
◼ Discrete-time signals are usually represented mathematically as sequences of numbers
n is an integer!!!
−= nnxx ]},[{
Discrete-Time Signals: Sampling
◼ In practice, discrete-time signals may arise from periodic sampling of analog signals
Discrete-Time Signals
◼ Mathematical representation
−= nnTxnx a ),(][
n is an integer and T is the sampling period
◼ Graphical Representation
x[n] - > y[n] = x[n/2]?
Not existing
0 1 2-1-2
-3-4-5 3 4 5
6
x[0]
x[2]
x[3]
x[-1]x[1]
Basic Operations of Sequences
◼ Product and Sum: sample-by-sample
0 1 2
3 4
x[0]
x[2]
x[1]
x[n]
0 1
2y[0]
y[2]
y[1]
3 4
y[n]
x[n] y[n]
0 1
2 3
4
x[n]+y[n]
0 1 2 3 4
Basic Operations of Sequences
◼ Multiplication a sequence by a number
multiplication of each sample value by
0 1 2
3 4
x[0]
x[2]
x[1]
x[n]0 1 2
3 42x[n]
Basic Operations of Sequences
◼ Delay or shift][][ 0nnxny −=
0
0
0
0
n
n
0 1 2
3 4
x[0]
x[2]
x[1]
x[n]
0 1 2 4
x[0]
x[2]
x[1]
x[n-2]
3
Basic Operations of Sequences
◼ Delay or shift
][][ nxny −= ][][ mnxny =
][][ 0nnxny −=0
0
0
0
n
n
0 1 2
3 4
x[0]
x[2]
x[1]
x[n]
0 1 2 4
x[0]
x[2]
x[1]
x[n-2]
3
Basic Sequences
◼ Unit sample sequence
◼ Often referred to as discrete-time impulse or impulse
=
=
.0,1
,0,0][
n
nn
0
1
◼ A delayed impulse
◼ Representing an arbitrary sequence using a sum of scaled, delayed impulses.
=
=−
.,1
,,0][
kn
knkn
]3[]1[]2[][ 312 −+−++= − nanananp
−=
−=k
knkxnx ][][][
◼ Represent a unit step sequence using impulses
−=
=
=
−=
+−+−+=
n
m
k
m
knnu
nnnnu
][
][][
...]2[]1[][][
0
0
1
?][ =n
Basic Sequences
◼ Sinusoidal sequence
with parameters real constants
-5 0 5 10 15 20 25-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
nallfornAnx ),cos(][ 0 +=
Page 16, Figure 2.5 cos ω0n for several different values of ω0. As ω0 increases from zero toward π (parts a-d), the
sequence oscillates more rapidly. As ω0 increases from π to 2π (parts d-a), the oscillations become slower.
Basic Sequences
◼ Exponential sequence (real)
If the parameters are real constants, the sequence is real.
-5 0 5 10 15 20 25-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
......
nallforAnx n ,][ =
1
◼ Exponential sequence (complex)
)sin()cos(
,][
00
)( 0
0
+++=
=
=
=
+
nAjnA
eA
eeA
andAcomplexforAnx
nn
njn
njnj
n
frequency phase1 =
nj
njnj
nj
nj
Ae
eAe
Aeny
Aenx
0
0
0
0
2
)2(][
][
=
=
=
=
+
][][ nynx =
r 20 +In a general case, when complex exponential sequences have frequencies of
, where r is an integer, those sequences are identical.
−
0
0 20
◼ E.g. 1
8
][
)4/cos(
)24/cos(
)4/)8(cos(]8[
),4/cos(][
=
=
=
+=
+=+
=
N
nx
n
n
nnx
nnx
)cos(
))(cos(][
)cos(][
00
0
0
NnA
NnANnx
nAnx
++=
++=+
+=
kN
kN
Nnxnx
)/2(
2
][][
0
0
=
=
+=
N and k integers
Or is rational0/2
The conditions for periodicity of sinusoidal
◼ E.g. 3 Find out the period of N
=8
=16
N
N
Differences from continuous time
Increasing does not decrease the period!0
[ ] cos( )
[ ] cos( /4 )
[ ] cos(3 /8 )
x n n
x n n
x n n
=
=
=
)cos(][
),cos(][
NnNnx
nnx
+=+
=
integer is ,2
][][
rrN
then
Nnxnx
if
=
+=
◼ The periodicity of sinusoidal and complex exponential sequences is dependent on their frequencies.
◼ A sequence without periodicity is called aperiodic.
Think and share…
◼ The discrete-time effect in life – how do you perceive the world or judge a
person?
Conclusions◼ Signals, digital signal processing◼ Discrete-time signals: sequences
Basic operations (product, sum, multiplication, and delay)Basic sequences (impulse, unit step sequence, real exponential sequence, complex exponential sequence, sinusoidal sequence, and periodic sequence)
◼ Next lecture: discrete-time systems & LTI systems
Assignment
◼ Preparation for the next lecture:
read p16-p30
◼ Do the self-test
◼ Solve the following problems
