102_1_Lecture17

102_1_Lecture17 - UCLA Spring 2009-2010 Systems and Signals...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Frequency Response The Laplace transform H ( s ) exists for any s = σ + j ω such that the Laplace transform integral converges. One important special case is when σ =0 , and s = j ω . This corresponds to the Fourier transform. It is also known as the frequency response H ( j ω ) of the system. ! ! s = j ! EE102: Systems and Signals; Spr 09-10, Lee 2
Background image of page 2
The j ω 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 speciFed 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
Background image of page 3

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

View Full DocumentRight Arrow Icon
Types of Filters Basic idea: Pass some signals at some frequencies, suppress others ! | H ( j ! ) ! ! ! Lowpass Highpass Bandpass Bandstop, or Notch EE102: Systems and Signals; Spr 09-10, Lee 4
Background image of page 4
Filter Terms | H ( j ! ) ! G p G s ! s Passband Transition Band Stopband Minimum Passband Gain Maximum Stopband Gain ! c EE102: Systems and Signals; Spr 09-10, Lee 5
Background image of page 5

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

View Full DocumentRight Arrow Icon
Ideal Filter Ideal lowpass flter 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
Background image of page 6
Impulse response (inverse Fourier transform) h ( t ) t but this is not causal. Two possible solutions for causal ±lter are: Truncate response symmetrically: linear phase and increased transition width t h ( t ) Common for discrete time ±lters (next quarter). EE102: Systems and Signals; Spr 09-10, Lee 7
Background image of page 7

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

View Full DocumentRight Arrow Icon
Non-linear phase (here, minimum phase) t h ( t ) Common for continuous time Flters (this quarter). To Fx up phase, can follow with an allpass flter . | 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
Background image of page 8
Functional Forms for Filters Conceptually, we can consider any impulse response to be a flter. Practically, we are going to consider flters that can be implemented as a discrete component circuit.
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 34

102_1_Lecture17 - UCLA Spring 2009-2010 Systems and Signals...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online