EEE 304, HW4
Problem 1:
Consider the transfer functions
1
1
,
??(??)
=
5?? 2 ? 2?? + 3
5?? 2 ? 2?? + 3
Determine their Tustin and FE equivalents for T = 0.1 (DT and CT respectively).
Comment on the frequency range that the frequency responses are expected to match and verify
using MATLAB.
??(??) =
Problem 2:
Suppose that a continuous time signal x(t) is processed by the following sampled-data system,
10
2
replacing an old analog filter with transfer function ?????? (??) = (??+10) .
1. Determine the DT transfer function approximating this CT filter using FE and Tustin
transformations.
2. Are the DT poles of FE and Tustin equivalents identical?
3. What would be an appropriate choice for the AAF cutoff?
x(t)
v(t)
y(t)
AAF
? cutoff
SAMPLING
10kHz
DT-Filter
H-DT(z)
Reconstruction
Problem 3:
Suppose that a discrete-time signal x(n) is processed by the discrete differentiator with transfer
???1
function ?????? (??) = ?? before sent to a ZOH at 10Hz and then a continuous time filter with
1
transfer function ?????? (??) = (??+1)(2??+1). Determine the DT transfer function of the system when
the output is also sampled at 10Hz.
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