Correlation of Discrete-Time Signals - Iowa State University

Correlation of Discrete-Time Signals - Iowa State University

Correlation of Discrete-Time Signals Transmitted Signal, x(n) Reflected Signal, y(n) = x(n-D) + w(n) 0 T Cross-Correlation Cross-correlation of x(n) and y(n) is a sequence, rxy(l) rxy l x n y n l l 0, 1, 2, n

rxy l x n l y n l 0, 1, 2, n Reversing the order, ryx(l) ryx l y n x n l l 0, 1, 2, n ryx l y n l x n n => rxy l ryx l l 0, 1, 2,

Similarity to Convolution No folding (time-reversal) rxy l x l y l In Matlab: Conv(x,fliplr(y)) ryx l y l x l Auto-Correlation Correlation of a signal with itself rxx l x n x n l rxx l l 0, 1, 2, n Used to differentiate the presence of a

like-signal, e.g., zero or one Even function Properties Two sequences, x(n) and y(n), with finite energy z n ax n by n l Find energy of z(n) 2 Ez ax n by n l n a 2 2 2

2 x n b y n l 2ab x n y n l n n a 2 rxx 0 b 2 ryy 0 2abrxy l 0 Ex Ey n Ez a 2 rxx 0 b 2 ryy 0 2abrxy l 0

(assume b 0) 2 a a rxx 0 2 rxy l ryy 0 0 b b Quadratric in (a/b) and positive, discriminant is non-negative: For crosscorrelation case: rxy l rxx 0 ryy 0 E x E y For autocorrelation case: rxx l rxx 0 Ex Maximum value occurs with zero lag (when signals are perfectly matched) Often normalized to range [-1,1]: xx l

rxy l rxx 0 ryy 0 xx l rxx l rxx 0 x n a nu n ; 0 a 1 rxx l x n x n l n n

a a n l n l 1 l a 1 a2 a l a

2n n l l 0 xx l rxx l l a rxx 0 l Periodic Sequences Power signals crosscorrelation: 1 r l lim x n y n l 2M 1

Define auto and crosscorrelations over one period of the signals If x(n) and y(n) are periodic signals with period N: 1 r l x n y n l N M xy M n M N1 xy n 0

Correlations are also periodic with period N y(n)=x(n)+w(n) LTI Systems Convolution, output of LTI system y n h n x n h k x n k k Crosscorrelation between the output and input signal: r l y l x l h l x l x l yx h l x l x l h l rxx l Similarly, input to output is: rxy l h l rxx l

Autocorrelation of output: ryy l y l y l h l x l h l x l h l h l x l x l rhh l rxx l ryy 0 rhh 0 rxx 0 rhh k rxx k k

Recently Viewed Presentations

  • Physics of Brownian Motors: Swimming in Molasses and

    Physics of Brownian Motors: Swimming in Molasses and

    What is a Brownian ratchet? Ultimately energy comes from chemical reaction, but the momentum Is borrowed from the thermal bath Three Key Features of Brownian Motor Mechanisms: spatial or temporal asymmetry external energy source thermal noise Brownian Motor Influencing intramolecular...
  • UW-Green Bay | Sheboygan Campus PowerPoint Theme 3

    UW-Green Bay | Sheboygan Campus PowerPoint Theme 3

    Is probably the best option for math and science classes, but is good for any class . Computer. Do not let yourself get distracted. Don't be online when you should be taking notes . Is a great option for English...
  • Understanding Text Structures - Liberty Hill J High School

    Understanding Text Structures - Liberty Hill J High School

    Chronological: find the signal words. Jane Goodall's work with chimpanzees has changed the world's attitudes towards our closest cousins. In 1957, she first went to Africa to observe chimpanzees in the wild and discovered their ability to make tools.
  • 3 Carbon and the Molecular Diversity of Life

    3 Carbon and the Molecular Diversity of Life

    When a carbon atom forms four single covalent bonds, the bonds angle toward the corners of an imaginary tetrahedron. ... Name. Ethane. Ethene ... Figure 3.4c Four ways that carbon skeletons can vary (part 3: double bond position)
  • Hvordan Lede De Som Ikke Vil Bli Ledet

    Hvordan Lede De Som Ikke Vil Bli Ledet

    Behovet for å være verdifull - selvaktelse, selvbilde - individuell egenverdi - sosial tilhørighet, selvkategorisering Sosialt stress for ledere Beslutnings- kvalitet Leder intelligens Leder erfaring Autocratic Leadership Transactional Leadership Charismatic Leadership Leader Leader Follower Follower Over-bearing authority Over-whelming ...
  • Prevention: Where we are now

    Prevention: Where we are now

    Building Bridges Across the Spectrum: How Prevention Connects with Addiction Treatment FACILITATED BY: JANE GOBLE-CLARK CENTER FOR PREVENTION SERVICES
  • Economic and Human Dimensions Research Associates ::.. Reframing

    Economic and Human Dimensions Research Associates ::.. Reframing

    At the Same Time, Acknowledgments. This presentation draws on the many ideas that have emerged from wide-ranging interactions and discussions with a variety of friends, colleagues, and collaborators—especially over the last six months.
  • PowerPoint Template

    PowerPoint Template

    One from each group will be chosen to be the exchange student, who will report what your group ordered. Closing Performance 9:00a- 12:00p, July 7th, 2011 Startalk故宫 &长城中文班 University of Virginia First scene Basic greetings, self introduction, family, and hobbies...