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Unformatted text preview: ECE600 Phil Schniter September 21, 2011 Introduction: • Much of modern engineering is concerned with signals and systems. • Roughly, a signal is an informationcontaining waveform (e.g., audio signal, image, digital video stream) and a system converts one waveform to another (e.g., low pass filter, mp3 encoder, a simple delay). • Many realworld signals live in a continuous domain (e.g., continuoustime), while much of modern signal processing is done via computation in a discrete domain. • In this course, we develop a solid understanding of signals/systems, especially the relationship between their continuous and discrete representations. The frequency domain will be of particular importance here. • This course is about understanding/applying concepts , not memorizing formulas, and mathematics is the language of these concepts. Thus, a major goal of this course is making you comfortable with the mathematics of signals and systems. 1 ECE600 Phil Schniter September 21, 2011 Outline: 1. Review of signals/systems background (a) Systems: linear, timeinvariant, causal, stable (b) Continuoustime transforms: FS, CTFT, Laplace (c) Discretetime transforms: DTFT, Ztransform 2. Sampling and reconstruction (a) sampling, aliasing, reconstruction (sinc & practical) (b) upsampling, downsampling, and rate conversion 3. Processing of finitelength signals (a) DFT, circ conv, windowing, spectral analysis (b) matrix/vector formulations (c) FFT, fast convolution, overlap/save 4. Design of discretetime filters (a) goals: magnitude, group delay, joint (b) FIR designs: window, minimax, leastsquares (c) IIR designs: bilinear transform, Prony’s method 2 ECE600 Phil Schniter September 21, 2011 Signals and systems: • Continuoustime: t ∈ R (the set of real numbers) { x ( t ) } H c { y ( t ) } signals: { x ( t ) } ∀ t and { y ( t ) } ∀ t system: H c • Discretetime: n ∈ Z (the set of integers) { x [ n ] } H { y [ n ] } signals: { x [ n ] } ∀ n and { y [ n ] } ∀ n system: H • Assumption: We assume that all signals are complex valued : x [ n ] = Re { x [ n ] } + j Im { x [ n ] } . • Uniform sampling: We say that { x [ n ] } is a Tsampled version of { x ( t ) } when x [ n ] = x ( nT ) for every integer n . Here, T denotes the sampling interval in seconds. • Key question: What “information” does the discretetime sequence { x [ n ] } ∀ n contain relative to the continuoustime waveform { x ( t ) } ∀ t ? 3 ECE600 Phil Schniter September 21, 2011 A few important system properties: For the statements below, assume that { y [ n ] } = H{ x [ n ] } . 1. Linear : ∀ α,β ∈ C , H{ αx [ n ]+ βw [ n ] } = α H{ x [ n ] } + β H{ w [ n ] } ....
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This note was uploaded on 10/29/2011 for the course ECE 600 taught by Professor Clymer,b during the Fall '08 term at Ohio State.
 Fall '08
 Clymer,B

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