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

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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...
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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.

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

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