Ch4(5) Simple Digital Filters.pdf

Simple Digital Filters Simple FIR Digital Filters
• Later in the course we shall review various • FIR digital filters considered here have
methods of designing frequency-selective integer-valued impulse response coefficients
filters satisfying prescribed specifications • These filters are employed in a number of
• We now describe several low-order FIR and practical applications, primarily because of
IIR digital filters with reasonable selective their simplicity, which makes them amenable
frequency responses that often are to inexpensive hardware implementations
satisfactory in a number of applications
1 2
Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Simple FIR Digital Filters Simple FIR Digital Filters
Lowpass FIR Digital Filters
• The simplest lowpass FIR digital filter is the • On the other hand, as w increases from 0 to
2-point moving-average filter given by p, the magnitude of the zero vector
decreases from a value of 2, the diameter of
z +1
H (z) = 1 (1+ z­1) = the unit circle, to 0
0 2
2z jw
• Hence, the magnitude response | H 0 ( e ) | is
• The above transfer function has a zero at a monotonically decreasing function of w
z = ­ 1 and a pole at z = 0 from w = 0 to w = p
• Note that here the pole vector has a unity
3 magnitude for all values of w 4
Copyright © 2001, S. K. Mitra Copyright © 2001, S. K. Mitra
Sim