《信号与系统教学资料》10-Magnitude and Phase.pptVIP

* * * * * * * * * * * * * * * Signals and Systems Spring 2014 Lecture #20 8 May, 2014 Chen Zubin (陈祖斌) Room 304, Geology Palace, 0431 czb@jlu.edu.cn Signals and Systems 1. Magnitude and Phase of FT, and Parseval Relation2. Linear and Nonlinear Phase3. Ideal and Nonideal Frequency-Selective Filters4. CT DT Rational Frequency Responses5. DT First-and Second-Order Systems 1. Magnitude and Phase of FT, and Parseval Relation CT Parseval Relation: DT Parseval Relation: Effects of Phase Not on signal energy distribution as a function of frequency Can have dramatic effect on signal shape/character — Constructive/Destructive interference Is that important? — Depends on the signal and the context Effects of Phase Demo: 1) Effect of phase on Fourier Series 2) Effect of phase on image processing Log-Magnitude and Phase Plotting Log-Magnitude and Phase a) For real-valued signals and systems Plot for ω ≥ 0, often with a logarithmic scale for frequency in CT b) In DT, need only plot for 0 ≤ ω ≤ π (with linear scale) c) For historical reasons, log-magnitude is usually plotted in units of decibels (dB): So... 20 dB or 2 bels: = 10 amplitude gain = 100 power gain Plotting Log-Magnitude and Phase A Typical Bode plot for a second-order CT system A typical plot of the magnitude and phase of a second- order DT frequency response 2. Linear and Nonlinear Phase Result : Linear phase ?simply a rigid shift in time, no distortion Nonlinear phase ?distortion as well as shift All-Pass Systems Demo: Impulse response and output of an all-pass system with nonlinear phase All-Pass Systems Group Delay How do we think about signal delay when the phase is nonlinear? CT Noncausal h(t 0) ≠0 Oscillatory Response —e.g. step response Ideal Lowpass Filter Ideal Lowpass Filter Rational Frequency Responses —Second-order system, has two energy storing elements, e.g. L and C If the system is described by LCCDE’s (Linear-Constant-Coefficien