Bài giảng Digital Signal Processing - Chapter 7: Digital Filter Realizations - Võ Trung Dũng

DSP-Chapter 7-Dr. Dung Trung Vo
Digital Signal Processing
Digital Filter Realizations
Dr. Dung Trung Vo
Telecommunication Divisions
Department of Electrical and Electronics
September, 2013
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Direct Form: considering a simple second-order filter with transfer function.
I/O difference equation
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Example: Draw the direct form realization of the following filter.
and determine corresponding difference equation and sample processing algorithm
Solution: The difference equation is:
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Canonical Form: (direct form II) divide the I/O equation into two subgroups: 
the recursive terms and the non-recursive ones
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Canonical Form: (direct form II) divide the I/O equation into two subgroups: 
the recursive terms and the non-recursive ones
Interchanging N(z) and 1/D(z)
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Canonical Form: (direct form II) divide the I/O equation into two subgroups: 
the recursive terms and the non-recursive ones
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 General canonical Form: Canonical realization form of Mth order IIR filter
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Cascade Form: The cascade realization form of a general transfer function 
assumes that the transfer function is the product of such second-order sections
A second-order section 
(SOS) is a second-order 
transfer function
DSP-Chapter 7-Dr. Dung Trung Vo
Digital Filter Realizations
 Example: Draw the cascade and canonical realizations of the following filter
DSP-Chapter 7-Dr. Dung Trung Vo
Equivalent Descriptions of Digital Filters
 Homeworks: 7.1->7.7, 7.10->7.12