Lec 17

# Lec 17 - UCLA Spring 2009-2010 Systems and Signals Lecture...

This preview shows pages 1–10. 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 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 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: UCLA Spring 2009-2010 Systems and Signals Lecture 17: Frequency Response, Bode Plots, and Filters May 26, 2010 EE102: Systems and Signals; Spr 09-10, Lee 1 Frequency Response The Laplace transform H ( s ) exists for any s = σ + jω such that the Laplace transform integral converges. One important special case is when σ = 0 , and s = jω . This corresponds to the Fourier transform. It is also known as the frequency response H ( jω ) of the system. ℜ ℑ s = j ω EE102: Systems and Signals; Spr 09-10, Lee 2 The jω axis may not be in the region of convergence, and the frequency response may not exist. If it does, the frequency response characterizes the system after the transients have died out, and the system is in steady state . We will consider two applications of frequency response: • Filter Design where we want to design a system with a specified frequency response • Feedback Control where we want to modify the frequency response of an existing system EE102: Systems and Signals; Spr 09-10, Lee 3 Types of Filters Basic idea: Pass some signals at some frequencies, suppress others ω | H ( j ω ) | ω | H ( j ω ) | ω | H ( j ω ) | ω | H ( j ω ) | Lowpass Highpass Bandpass Bandstop, or Notch EE102: Systems and Signals; Spr 09-10, Lee 4 Filter Terms | H ( j ω ) | ω G p G s ω s Passband Transition Band Stopband Minimum Passband Gain Maximum Stopband Gain ω c EE102: Systems and Signals; Spr 09-10, Lee 5 Ideal Filter Ideal lowpass filter is distortionless over a frequency band: | H ( f ) | f ∠ H ( f ) f Unity passband with linear phase. A signal within the passband is delayed, but undistorted in amplitude or phase. EE102: Systems and Signals; Spr 09-10, Lee 6 Impulse response (inverse Fourier transform) h ( t ) t but this is not causal. Two possible solutions for causal filter are: • Truncate response symmetrically: linear phase and increased transition width t h ( t ) Common for discrete time filters (next quarter). EE102: Systems and Signals; Spr 09-10, Lee 7 • Non-linear phase (here, minimum phase) t h ( t ) Common for continuous time filters (this quarter). To fix up phase, can follow with an allpass filter . | H ( f ) | f ∠ H ( f ) f Truncated, Linear Phase | H ( f ) | f ∠ H ( f ) f Non-linear Phase EE102: Systems and Signals; Spr 09-10, Lee 8 Functional Forms for Filters • Conceptually, we can consider any impulse response to be a filter. • Practically, we are going to consider filters that can be implemented as a discrete component circuit. • This means that the frequency response is a rational function ....
View Full Document

## This note was uploaded on 10/21/2010 for the course EE ee102 taught by Professor Levan during the Spring '09 term at UCLA.

### Page1 / 34

Lec 17 - UCLA Spring 2009-2010 Systems and Signals Lecture...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online