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ECE 2026 - 29 Feb - 4 Mar Book Notes

by: Connor Hawley

ECE 2026 - 29 Feb - 4 Mar Book Notes ECE 2026 A

Connor Hawley

GPA 4.0
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About this Document

On Interpreting the titles: For lecture notes: L means lecture M means Monday, T means Tuesday, W means Wednesday, R means Thursday, and F means Friday. For book notes: Ch. means chapter Sc. means ...
Intro Signal Processing
Dr. Mark A. Clements
Class Notes
intro, Digital, signal, processing, ECE, 2026




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This 3 page Class Notes was uploaded by Connor Hawley on Sunday March 6, 2016. The Class Notes belongs to ECE 2026 A at Georgia Institute of Technology - Main Campus taught by Dr. Mark A. Clements in Winter 2016. Since its upload, it has received 28 views. For similar materials see Intro Signal Processing in Electrical Engineering at Georgia Institute of Technology - Main Campus.


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Date Created: 03/06/16
Ch. 5 Sc. 5 - 7 Tuesday, March 1, 2016 11:45 AM Chapter 5 - FIR Filters Section 5 - Implementation of FIR filters - Three basic building blocks are needed to build FIR filters ○ Multiplier -  The impulse response is simply ○ Adder ○ Unit delay - We use block diagram notation to graphically represent complexstructures - For example, here is a feed forward difference equation's implementation - This is also a third-order FIR filter ○ The standard structure is called direct form - Every implementationhas a transposed form, too Section 6 - Linear-Time Invariant (LTI)Systems - Discusses two general properties of systems:linearity and time invariance - We first list some basic systems - We first list some basic systems ○ Square-law system - - Time invariance - when an input is delayed (shifted) by , the output is shifted by the same amount ○ To verify that a system is time-invariant,check that    Here, since both outputs are the same, the system is time-invariantby checking the interchange of operations - Linearity - linear systemshave the property that if and , then ○ ○ This is also called the principle of superposition ○ Linearity can similarly be proven using the interchange of operations - Systems that are both linear and time-invariant are called LTI systems ○ FIR filters are all LTI systems Section 7 - Convolution and LTI Systems - The impulse response is a complete characterization for any LTI system - Convolutionis the general formula that allows us to computethe output from the input for any LTI system - Somehow,a convolutionsum formula is derived ○ ○ All LTI systemscan be represented by a convolution sum - Properties ○ Commutative - Identity element of convolution ○ Identity element of convolution ○ Associative - ○ Distributive -


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