This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lesson 13 Lesson 13 Challenge 12 Lesson 13: Frequency response function Challenge 13: Lesson 13 Challenge 12 A linear timeinvariant system is assembled by cascading two MA filters. The 1 st stage is a 5 th order MA filter. The 2 nd stage is a 7 th order MA filter. What is the overall impulse response of the cascade system. Let h 1 =(1/5)[1,1,1,1,1] Let h 2 =(1/7)[1,1,1,1,1,1,1] h=h 1 *h 2 = (1/35)[1 2 3 4 5 5 5 4 3 2 1] The length of h is (5+71)=11 samples, with a length 4 sample transition buildup, length 4 sample transition builddown, and length 3 steadystate interval. Lesson 13 Challenge 12 H 1 (e j ω ) H 2 (e j ω ) Lesson 13 Challenge 12 H 1 (e j ω ) H 2 (e j ω ) Combined (Cascaded) Notice location of the nulls. Lesson 13 Lesson 13 Consider an LTI system having a known impulse response. The output is defined by the convolution sum: Suppose the input is with a signal of magnitude A, normalize frequency ω , and phase offset φ . [ ] [ ] k n x h n y N k k = ∑ = [ ] ( 29 π ω π ϖ ω φ ω < ≤ = = + : / ; s n j T Ae n x Lesson 13 Lesson 13 Convolution: (N+1)order FIR and x[k] Define: frequency response function or simply frequency response . for inputs x[k] (complex exponentials) [ ] ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 n j j n j j k j N k k k j n j j N k k k n j N k k e Ae e Ae e h e e Ae h Ae h n y ω φ ω φ ω ω ω φ φ ω ω ℑ = = = = = = + = ∑ ∑ ∑ ( 29 ( 29 ( 29 C ∈ = = ℑ = ∑ k j N k k j e h e H ω ω ω Lesson 13 Lesson 13 Outcome: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 C C C ∈ + =...
View
Full
Document
This note was uploaded on 08/21/2010 for the course EEL 3135 taught by Professor ? during the Spring '08 term at University of Florida.
 Spring '08
 ?
 Frequency

Click to edit the document details