View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Chapter 2. Discrete-Time Signals and Systems PowerPoint presentation | free to download - id: 1d5a57-ZDc1Z

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Chapter 2. Discrete-Time Signals and Systems

- Gao Xinbo
- School of E.E., Xidian Univ.
- Xbgao_at_ieee.org
- http//see.xidian.edu.cn/teach/matlabdsp/

Main Contents

- Important types of signals and their operations
- Linear and shift-invariant system
- Easier to analyze and implement
- The convolution and difference equation

representations - Representations and implementation of signal and

systems using MATLAB

Discrete-time signals

- Analog and discrete signals
- analog signal
- t represents any physical quantity, time in sec.
- Discrete signal discrete-time signal
- N is integer valued, represents discrete

instances in times

Discrete-time signal

- In Matlab, a finite-duration sequence

representation requires two vectors, and each for

x and n. - Example
- Question whether or not an arbitrary

infinite-duration sequence can be represented in

MATLAB?

Types of sequences

- Elementary sequence for analysis purposes
- 1. Unit sample sequence
- Representation in MATLAB

Function x,nimpseq(n0,n1,n2)

- A nn1n2
- x zeros(1,n2-n11) x(n0-n11)1
- B nn1n2 x (n-n0)0 stem(n,x,ro)

2. Unit step sequence

A nn1n2 xzeros(1,n2-n21)

x(n0-n11end)1 B nn1n2 x(n-n0)gt0

3. Real-valued exponential sequence

For Example

n010 x(0.9).n stem(n,x,ro)

4. Complex-valued exponential sequence

Attenuation ???? frequency in radians For

Example n010 xexp((23j)n)

5. Sinusoidal sequence

Phase in radians For Example n010

x3cos(0.1pinpi/3)2sin(0.5pin)

6. Random sequence

- Rand(1,N)
- Generate a length N random sequence whose

elements are uniformly distributed between 0,1 - Randn(1,N)
- Generate a length N Gaussian random sequence with

mean 0 and variance 1. en 0,1

7. Periodic sequence

- A sequence x(n) is periodic if x(n)x(nN)
- The smallest integer N is called the fundamental

period - For example
- A xtildex,x,x,x
- B xtildexones(1,P) xtildextilde()

xtildextilde transposition

Operations on sequence

- 1. Signal addition
- Sample-by-sample addition
- x1(n)x2(n)x1(n)x2(n)

Function y,nsigadd(x1,n1,x2,n2) nmin(min(n1),m

in(n2)) max(max(n1),max(n2)) y1zeros(1,length(n

)) y2y1 y1(find((ngtmin(n1))

(nltmax(n1))1))x1 y2(find((ngtmin(n2))

(nltmax(n2))1))x2 Yy1 y2

2. Signal multiplication

- Sample-by-sample multiplication
- Dot multiplication
- x1(n).x2(n)x1(n) x2(n)

Function y,nsigmult(x1,n1,x2,n2) nmin(min(n1),

min(n2)) max(max(n1),max(n2)) y1zeros(1,length

(n)) y2y1 y1(find((ngtmin(n1))

(nltmax(n1))1))x1 y2(find((ngtmin(n2))

(nltmax(n2))1))x2 Yy1 . y2

3. Scaling

- ax(n)ax(n)

4. Shifting

- y(n)x(n-k)
- mn-k yx

5. folding

- y(n)x(-n)
- yfliplr(x) n-fliplr(n)

6. Sample summation ss

sum(x(n1n2) 7. Sample production sp

prod(x(n1n2))

8. Signal energy se sum(x . conj(x))

or se sum(abs(x) . 2) 9. Signal power

Examples

- Ex020100 composite basic sequences
- Ex020200 operation on sequences
- Ex020300 complex sequence generation
- Ex020400 even-odd decomposition

Some useful results

- Unit sample synthesis
- Any arbitrary sequence can be synthesized as a

weighted sum of delayed and scaled unit sample

sequence. - Even and odd synthesis
- Even (symmetric) xe(-n)xe(n)
- Odd (antisymmetric) xo(-n)-xo(n)
- Any arbitrary real-valued sequence can be

decomposed into its even and odd component x

(n)xe(n) xo(n)

Function xe, x0, m evenodd(x,n) If

any(imag(x) 0) error(x is not a real

sequence) End m -fliplr(n) m1 min(m,n)

m2 max(m,n) mm1m2 nm n(1)-m(1) n1

1length(n) x1 zeros(1, length(m)) x1(n1nm)

x x x1 xe 0.5 (x flipflr(x)) xo

0.5(x - fliplr(x))

The geometric series

- A one-side exponential sequence of the form an,

ngt0, where a is an arbitrary constant, is

called a geometric series. - Expression for the sum of any finite number of

terms of the series

Correlations of sequences

- It is a measure of the degree to which two

sequences are similar. Given two real-valued

sequences x(n) and y(n) of finite energy, - Crosscorrelation
- Autocorrelation

The index l is called the shift or lag parameter.

The special case y(n)x(n)

Discrete Systems

- Mathematically, an operation T.
- y(n) T x(n)
- x(n) excitation, input signal
- y(n) response, output signal
- Classification
- Linear systems
- Nonlinear systems

Linear operation L.

- Iff L. satisfies the principle of superposition
- The output y(n) of a linear system to an

arbitrary input x(n) - is called impulse response, and is

denoted by h(n,k)

h(n,k) the time-varying impulse response

Linear time-invariant (LTI) system

- A linear system in which an input-output pair is

invariant to a shift n in time is called a linear

times-invariant system - y(n) Lx(n) ---? y(n-k) Lx(n-k)
- The output of a LTI system is call a linear

convolution sum - An LTI system is completely characterized in the

time domain by the impulse response h(n).

Properties of the LTI system

- Stability
- A system is said to be bounded-input

bounded-output (BIBO) stable if every bounded

input produces a bounded output. - Condition absolutely summable
- To avoid building harmful systems or to avoid

burnout or saturation in system operation

Properties of the LTI system

- Causality
- A system is said to be causal if the output at

index n0 depends only on the input up to and

including the index n0 - The output does not depend on the future values

of the input - Condition h(n) 0, n lt 0
- Such a sequence is termed a causal sequence.
- To make sure that systems can be built.

Convolution

- Convolution can be evaluated in many different

ways - If the sequences are mathematical functions, then

we can analytically evaluate x(n)h(n) for all n

to obtain a functional form of y(n) - Graphical interpretation, folded-and-shifted

version - Matlab implementation
- Function y,nyconv_m(x,nx,h,nh)
- nyb nx(1)nh(1) nye nx(length(x))nh(length(h

)) - ny nybnye
- n conv(x,h)

Function form of convolution

Three different conditions under which u(n-k) can

be evaluated Case 1 nlt0 the nonzero

values of x(n)and y(n) do not overlap. Case 2

0ltnlt9 partially overlaps Case 3 ngt9

completely overlaps

Folded-and-shifted

- Signals xx(1),x(2),x(3),x(4),x(5)
- System Impulse Response hh(1),h(2)h(3),h(4)
- yconv(x,h)
- y(1)x(1)h(1) y(2)x(1)h(2)x(2)h(1)
- y(3)x(1)h(3)x(2)h(2)x(3)h(1)
- x(1),x(2),x(3),x(4),x(5)

- h(4),h(3),h(2),h(1)

Note that the resulting sequence y(n) has a

longer length than both the x(n) and h(n)

sequence.

(No Transcript)

Sequence correlations revisited

- The correlation can be computed using the conv

function if sequences are of finite duration. - Example 2.8
- The meaning of the crosscorrelation
- This approach can be used in applications like

radar signal processing in identifying and

localizing targets.

Difference Equation

- An LTI discrete system can also be described by a

linear constant coefficient difference equation

of the form - If aN 0, then the difference equation is of

order N - It describes a recursive approach for computing

the current output,given the input values and

previously computed output values.

Solution of difference equation

- y(n) yH(n) yP(n)
- Homogeneous part yH(n)
- Particular part yP(n)
- Analytical approach using Z-transform will be

discussed in Chapter 4 - Numerical solution with Matlab
- y filter(b,a,x)
- Example 2.9

Zero-input and Zero-state response

- In DSP the difference equation is generally

solved forward in time from n0. Therefore

initial conditions on x(n) and y(n) are necessary

to determine the output for ngt0. - Subject to the initial conditions

Solution

Zero-input and Zero-state response

- yZI(n) zero-input solution
- A solution due to the initial conditions alone
- yZS(n) zero-state solution
- A solution due to input x(n) alone

Digital filter

- Discrete-time LTI systems are also called digital

filter. - Classification
- FIR filter IIR filter
- FIR filter
- Finite-duration impulse response filter
- Causal FIR filter
- h(0)b0,,h(M)bM
- Nonrecursive or moving average (MA) filter
- Difference equation coefficients, bm and a01
- Implementation in Matlab Conv(x,h) filter(b,1,x)

IIR filter

- Infinite-duration impulse response filter
- Difference equation
- Recursive filter, in which the output y(n) is

recursively computed from its previously computed

values - Autoregressive (AR) filter

ARMA filter

- Generalized IIR filter
- It has two parts MA part and AR part
- Autoregressive moving average filter, ARMA
- Solution
- filter(b,a,x) bm, ak

Reference and Assignment

- Textbook pp1 to pp35
- Chinese reference book pp1 to pp18
- ???????????????(???),?????,2001?1?
- Exercises
- Textbook p2.1b,c p2.2b,d ?2.5
- Textbook P2.12b, 2.15, 2.17b, ?2.8

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Chapter 2. Discrete-Time Signals and Systems" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Xidian University and other schools with their online training by sharing educational presentations for free