Lesson_32

# Lesson_32 - Lesson 32 Lesson 32 Challenge 31 Lesson 32 –...

This preview shows pages 1–8. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document

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.

Unformatted text preview: Lesson 32 Lesson 32 Challenge 31 Lesson 32 – Lowpass Filters Challenge 32 Lesson 32 Challenge 31 A Fourier series w.r.t. basis functions φ k (t) is given by: Orthogonality requires: t jk k k k k e t t a t x ) ( ; ) ( ) ( ϖ φ φ = = ∑ ∞-∞ = n m if d t t T n m n m ≠ = = ∫ * ) ( ) ( ) ( ), ( τ τ φ τ φ φ φ Lesson 32 Challenge 30 Computing: otherwise n m if T d e d e e d t t T n m j T jn jm T n m n m , * ) ( ) ( ) ( ), ( ) ( = = = = = ∫ ∫ ∫-- τ τ τ τ φ τ φ φ φ τ ϖ τ ϖ τ ϖ a b 1 a 1 To illustrate, consider x(t)=1+1.414cos( ϖ t+45 ° ) =1+cos( ϖ t)+sin( ϖ t). Tthe Fourier series coefficients are: a =1, a 1 =1, b 1 =1, all others equal zero. Lesson 32 Lesson 32 Continuous-time frequency selective electronic filters have been designed for nearly a century in a consistent manner using the same baseline theory. The only substantial difference is today the design have been reduced to a computer program. Descriptions: ODE, impulse response, Laplace transform, Frequency response They are generally of low order and can be assembled from simple filter sections configured as a cascade (multiplicative) or parallel (additive) structure. Lesson 32 Lesson 32 An ideal delay has a frequency response How do I build a continuous-time time delay? Fixed length conductor SAW ADC/DAC ( 29 T j e j H ϖ ϖ- = Lesson 32 Lesson 32 Running Integrator Circuit h + (t) = δ (t) – δ (t-T ) h I (t) = u(t) h(t) = ( δ (t) – δ (t-T )) u(t) = u(t)-u(t-T ) ∈ = otherwise T t for t h ] , [ 1 ) ( Lesson 32 Lesson 32 ( 29 ( 29 ( 29 2 / 2 / 2 / sin T j e T j H ϖ...
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.

### Page1 / 30

Lesson_32 - Lesson 32 Lesson 32 Challenge 31 Lesson 32 –...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online