filters - EE236A (Fall 2007-08) Lecture 6 FIR filter design...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE236A (Fall 2007-08) Lecture 6 FIR filter design • FIR filters • linear phase filter design • magnitude filter design • equalizer design 6–1 FIR filters finite impulse response (FIR) filter: y ( t ) = n − 1 summationdisplay τ =0 h τ u ( t − τ ) , t ∈ Z • u : Z → R is input signal ; y : Z → R is output signal • h i ∈ R are called filter coefficients ; n is filter order or length filter frequency response: H : R → C H ( ω ) = h + h 1 e − jω + ··· + h n − 1 e − j ( n − 1) ω = n − 1 summationdisplay t =0 h t cos tω − j n − 1 summationdisplay t =0 h t sin tω ( j = √ − 1) periodic, conjugate symmetric, so only need to know/specify for ≤ ω ≤ π FIR filter design problem: choose h so H and h satisfy/optimize specs FIR filter design 6–2 example: (lowpass) FIR filter, order n = 21 impulse response h : 2 4 6 8 10 12 14 16 18 20-0.2-0.1 0.1 0.2 t h ( t ) frequency response magnitude | H ( ω ) | and phase negationslash H ( ω ) : 0.5 1 1.5 2 2.5 3 10-3 10-2 10-1 10 10 1 ω | H ( ω ) | 0.5 1 1.5 2 2.5 3-3-2-1 1 2 3 ω negationslash H ( ω ) FIR filter design 6–3 Linear phase filters suppose n = 2 N + 1 is odd and impulse response is symmetric about midpoint: h t = h n − 1 − t , t = 0 , . . . , n − 1 then H ( ω ) = h + h 1 e − jω + ··· + h n − 1 e − j ( n − 1) ω = e − jNω (2 h cos Nω + 2 h 1 cos( N − 1) ω + ··· + h N ) = e − jNω tildewide H ( ω ) • term e − jNω represents N-sample delay • tildewide H ( ω ) is real • | H ( ω ) | = | tildewide H ( ω ) | called linear phase filter ( negationslash H ( ω ) is linear except for jumps of ± π ) FIR filter design 6–4 Lowpass filter specifications ω δ 1 1 /δ 1 δ 2 ω p ω s π specifications: • maximum passband ripple ( ± 20 log 10 δ 1 in dB): 1 /δ 1 ≤ | H ( ω ) | ≤ δ 1 , ≤ ω ≤ ω p • minimum stopband attenuation ( − 20 log 10 δ 2 in dB): | H ( ω ) | ≤ δ 2 , ω s ≤ ω ≤ π...
View Full Document

This note was uploaded on 09/26/2009 for the course CAAM 236 taught by Professor Dr.vandenber during the Spring '07 term at Monmouth IL.

Page1 / 10

filters - EE236A (Fall 2007-08) Lecture 6 FIR filter design...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online