2025-L11su09

2025-L11su09 - 1 © 2003 JH McClel an& RW Schafer 1...

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Unformatted text preview: 1 6/9/2009 © 2003, JH McClel an & RW Schafer 1 ECE2025 Summer 2009 Lecture 11 Frequency Response of FIR Filters 15 Jun 09 6/9/2009 © 2003, JH McClel an & RW Schafer 3 ANNOUNCEMENTS ¡ June 15-16: ¡ Turn in HW #4 ¡ June 24-25: ¡ Turn in Lab #4 ¡ Do Lab #5 6/9/2009 © 2003, JH McClel an & RW Schafer 4 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 6, Sections 6-1, 6-2, 6-3, 6-4, & 6-5 ¡ Other Reading: ¡ Recitation: Chapter 6 ¡ FREQUENCY RESPONSE EXAMPLES ¡ Next Lecture: Chap. 6, Sects. 6-6, 6-7 & 6-8 6/9/2009 © 2003, JH McClel an & RW Schafer 5 ∑ = − = M k k n x k h n y ] [ ] [ ] [ Last Class: Convolution Sum ¡ Output = Convolution of x[n] & h[n] Output = Convolution of x[n] & h[n] ¡ NOTATION: ¡ Here is the FIR case: FINITE LIMITS FINITE LIMITS Same as b k ] [ ] [ ] [ n x n h n y ∗ = 2 6/9/2009 © 2003, JH McClel an & RW Schafer 6 LTI SYSTEMS ¡ LTI: L inear & T ime- I nvariant ¡ COMPLETELY CHARACTERIZED by: ¡ IMPULSE RESPONSE h[n] ¡ CONVOLUTION : y[n] = x[n]* h[n] ¡ The “rule”defining the system can ALWAYS be re- written as convolution ¡ FIR Example: h[n] is same as b k 6/9/2009 © 2003, JH McClel an & RW Schafer 7 FIR Filter “Convolution Reverbs” Waves IR-1 ¡ “Plug-in” for digital audio workstation software 6/9/2009 © 2003, JH McClel an & RW Schafer 8 FIR Filter “Convolution Reverbs” Space Designer ¡ Part of Emagic (now Apple) “Logic Pro” digital audio sequencing software 6/9/2009 © 2003, JH McClel an & RW Schafer 9 New material LECTURE OBJECTIVES ¡ SINUSOIDAL INPUT SIGNAL ¡ DETERMINE the FIR FILTER OUTPUT ¡ FREQUENCY RESPONSE of FIR ¡ PLOTTING vs. Frequency ¡ MAGNITUDE vs. Freq ¡ PHASE vs. Freq ) ( ˆ ˆ ˆ ) ( ) ( ω ω ω j e H j j j e e H e H ∠ = MAG PHASE 3 6/9/2009 © 2003, JH McClel an & RW Schafer 10 DOMAINS: Time & Frequency ¡ Time-Domain: “n” = time ¡ x[n] discrete-time signal ¡ x(t) continuous-time signal ¡ Frequency Domain (sum of sinusoids)...
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2025-L11su09 - 1 © 2003 JH McClel an& RW Schafer 1...

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