{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture23

lecture23 - EE313 Linear Systems and Signals Fall 2010...

This preview shows pages 1–6. Sign up to view the full content.

EE313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Frequency Response of Discrete-Time Systems

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
23 - 2 Complex Exponentials Two-sided complex exponential z n when input into LTI systems Output will be same complex exponential weighted by H ( z ) Provided that z is in region of convergence for H ( z ) When we specialize the z -domain to frequency domain, the magnitude of H ( z ) will control which frequencies are attenuated or passed [ ] [ ] [ ] [ ] [ ] ) ( ] [ z H z z m h z z m h z n h n x n h n y n m m n m m n n = = = = = -∞ = - -∞ = -
23 - 3 Frequency Response for LTI Systems Continuous time Discrete time Real-valued impulse response: H ( e - j ω ) = H* ( e j ω ) Input Output ( 29 ( 29 ( 29 ( 29 ( 29 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ) ( ) ( cos 2 j j k j e H j j k j e H j j e H ω k e H e e e H e e e H j j + = + = - - ) cos( 2 k e e k j k j ϖ ϖ ϖ = + - ] [ k h k j e ϖ ( 29 k j j e e H ϖ ϖ ( 29 k cos ϖ ( 29 ( 29 ( 29 ϖ ϖ ϖ cos j j e H k e H + ) ( t h t j e ( 29 t j e j H ( 29 ( 29 ( 29 + j H t j H cos ( 29 t cos ( 29 ( 29 ( 29 ( 29 k j j k j j k j j k j j e e H e e H e e H e e H * ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ + = + - - -

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
23 - 4 Response to Sampled Sinusoids Start with a continuous-time sinusoid Sample it every T s seconds ( see slide 7-6 ) We show discrete-time sinusoid with Resulting in Discrete-time frequency is equal to continuous- time frequency multiplied by sampling period ( 29 t t x cos ) ( ϖ = ( 29 s nT t T n t x n x s cos ) ( ] [ ϖ = = = ( 29 ( 29 n T n s cos cos ϖ = s T ϖ =
23 - 5 Example

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 16

lecture23 - EE313 Linear Systems and Signals Fall 2010...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online