tailieunhanh - Lecture Digital signal processing: Lecture 8 - Zheng-Hua Tan

Lecture 8 - FIR Filter Design include all of the following content: FIR filter design, commonly used windows, generalized linear-phase FIR filter, the Kaiser window filter design method. | Digital Signal Processing Fall 2006 Lecture 8 FIR Filter Design Zheng-Hua Tan Department of Electronic Systems Aalborg University Denmark zt@ 1 Digital Signal Processing VIII Zheng-Hua Tan 2006 AALBORG UNIVERSITY Course at a glance MM3 MM9 MM10 2 Digital Signal Processing VIII Zheng-Hua Tan 2006 1 FIR filter design h n Design problem the FIR system function H z 2 bkz - k k 0 bn 0 n M 0 otherwise Start from impulse response directly H z h 0 h 1 z-1 . h M z M Find the degree M and the filter coefficients h k to approximate a desired frequency response 3 Digital Signal Processing VIII Zheng-Hua Tan 2006 Part I FIR filter design FIR filter design Commonly used windows Generalized linear-phase FIR filter The Kaiser window filter design method 4 Digital Signal Processing VIII Zheng-Hua Tan 2006 2 Lowpass filter - as an example Ideal lowpass filter TT iax 1 a a Hlp e ln 0 rnc n sin an h n - OT n OT nn IIR filter based on transformations of continuous- time IIR system into discrete-time ones. 1 Hc jQ l 1 Q Q c 2 N poles Figure Dependence of Butterworth magnitude characteristics on the order N. FIR filter how h n is non-causal infinite . 5 Digital Signal Processing VIII Zheng-Hua Tan 2006 AALBORG UNIVERSITY Design by windowing Desired frequency responses are often piecewiseconstant with discontinuities at the boundaries between bands resulting in non-causal and infinte impulse response extending from - OT to 00 but n OT hd n 0 So the most straightforward method is to truncate the ideal response by windowing and do time- shifting g n hd .n n M 0 otherwise h n g n - M 6 Digital Signal Processing VIII Zheng-Hua Tan 2006 AALBORG UNIVERSITY