Simple Digital Filters Later in the course we shall review various methods of designing frequency-selective filters satisfying prescribed specifications We now describe several low-order fr and IIr digitalfilters with reasonable selective frequency responses that often are satisfactory in a number of applications Copyright C 2001, S K. Mitra
Copyright © 2001, S. K. Mitra 1 Simple Digital Filters • Later in the course we shall review various methods of designing frequency-selective filters satisfying prescribed specifications • We now describe several low-order FIR and IIR digital filters with reasonable selective frequency responses that often are satisfactory in a number of applications
Simple FIR Digital Filters Fir digital filters considered here have integer-valued impulse response coefficients These filters are employed in a number of practical applications, primarily because of their simplicity, which makes them amenable to inexpensive hardware implementations Copyright C 2001, S K. Mitra
Copyright © 2001, S. K. Mitra 2 Simple FIR Digital Filters • FIR digital filters considered here have integer-valued impulse response coefficients • These filters are employed in a number of practical applications, primarily because of their simplicity, which makes them amenable to inexpensive hardware implementations
Simple FIR Digital Filters Lowpass Fir digital Filters The simplest lowpass Fir digital filter is the 2-point moving-average filter given by H)=(1+=-2) z+1 2z The above transfer function has a zero at z=-l and a pole at z=0 Note that here the pole vector has a unity magnitude for all values of o 3 Copyright C 2001, S K. Mitra
Copyright © 2001, S. K. Mitra 3 Simple FIR Digital Filters Lowpass FIR Digital Filters • The simplest lowpass FIR digital filter is the 2-point moving-average filter given by • The above transfer function has a zero at and a pole at z = 0 • Note that here the pole vector has a unity magnitude for all values of w z z H z z 2 1 1 1 2 1 0 + = + = − ( ) ( ) z = −1
Simple FIR Digital Filters On the other hand as o increases from o to T the magnitude of the zero vector decreases from a value of 2 the diameter of the unit circle to o Hence, the magnitude response Ho(e) is a monotonically decreasing function of a from o=o to O=u 4 Copyright C 2001, S K. Mitra
Copyright © 2001, S. K. Mitra 4 Simple FIR Digital Filters • On the other hand, as w increases from 0 to p, the magnitude of the zero vector decreases from a value of 2, the diameter of the unit circle, to 0 • Hence, the magnitude response is a monotonically decreasing function of w from w = 0 to w = p | ( )| 0 jw H e
Simple FIR Digital Filters The maximum value of the magnitude function is 1 at o=0 and the minimum value is0atO=π,e, (e0)=1,|H(ez)=0 The frequency response of the above filter Is given by ho(ejo)=e jo/2 cos(@/2) Copyright C 2001, S K. Mitra
Copyright © 2001, S. K. Mitra 5 Simple FIR Digital Filters • The maximum value of the magnitude function is 1 at w = 0, and the minimum value is 0 at w = p, i.e., • The frequency response of the above filter is given by 1 0 0 0 | 0 ( )| = , | ( )| = j jp H e H e ( ) cos( / 2) / 2 0 = w jw − jw H e e