review

# review - ECE-600 Phil Schniter Introduction • Much of...

This preview shows pages 1–5. Sign up to view the full content.

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE-600 Phil Schniter September 21, 2011 Introduction: • Much of modern engineering is concerned with signals and systems. • Roughly, a signal is an information-containing 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 real-world signals live in a continuous domain (e.g., continuous-time), 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 ECE-600 Phil Schniter September 21, 2011 Outline: 1. Review of signals/systems background (a) Systems: linear, time-invariant, causal, stable (b) Continuous-time transforms: FS, CTFT, Laplace (c) Discrete-time transforms: DTFT, Z-transform 2. Sampling and reconstruction (a) sampling, aliasing, reconstruction (sinc & practical) (b) upsampling, downsampling, and rate conversion 3. Processing of finite-length signals (a) DFT, circ conv, windowing, spectral analysis (b) matrix/vector formulations (c) FFT, fast convolution, overlap/save 4. Design of discrete-time filters (a) goals: magnitude, group delay, joint (b) FIR designs: window, minimax, least-squares (c) IIR designs: bilinear transform, Prony’s method 2 ECE-600 Phil Schniter September 21, 2011 Signals and systems: • Continuous-time: t ∈ R (the set of real numbers) { x ( t ) } H c { y ( t ) } signals: { x ( t ) } ∀ t and { y ( t ) } ∀ t system: H c • Discrete-time: 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 T-sampled 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 discrete-time sequence { x [ n ] } ∀ n contain relative to the continuous-time waveform { x ( t ) } ∀ t ? 3 ECE-600 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 ] } ....
View Full Document

## 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.

### Page1 / 33

review - ECE-600 Phil Schniter Introduction • Much of...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online