DSP First, 2/e
Lecture 24 Time-Domain Response
for IIR Systems
Aug 2016 © 2003-2016, JH McClellan & RW Schafer 1
LECTURE OBJECTIVES
§ Calculate output from Input
§ Transient and Steady State Responses
§ Z-Transform method with Partial Fraction Expansion
§ SECOND-ORDER IIR FILTERS § TWO FEEDBACK TERMS
§ H(z) can have COMPLEX POLES & ZEROS
Aug 2016 © 2003-2016, JH McClellan & RW Schafer 4
å2 y[n]=a1y[n-1]+a2y[n-2]+ bkx[n-k]
k=0
READING ASSIGNMENTS
§ This Lecture:
§ Chapter 10, Sects. 10-9, 10-10, & 10-11
§ Partial Fraction Expansion
Aug 2016 © 2003-2016, JH McClellan & RW Schafer 3
CASCADE: Pole-Zero Cancellation
§ Multiply the z-transforms
x[n] v[n] y[n]
v[n]= x[n]+0.5x[n-1]-0.5x[n-2]
H 2 ( z ) = 1 – z -1
x[n] = u[n] + (0.5)n u[n]
Aug 2016 © 2003-2016, JH McClellan & RW Schafer 5
H1(z)
H2(z)
y[n] = ?
What is Frequency Response?
§ Sinusoid-in gives sinusoid-out
§ True for LTI systems
§ Seems to require an infinite-length sinusoid
x[n]=cos(wˆ0n) for -¥