Digital Signal Processing Reference
In-Depth Information
10
0
1
−10
0
0
10
20
30
40
50
60
−1
(b) Sample Number of Real Output
10
0
20
40
60
(a) Sample Number of Input
0
+
−10
Input (Real)
0
10
20
30
40
50
60
(c) Sample Number of Imaginary Output
10
10
9
1
0.5
0
0.9
−0.5
−1
−1
0
1
Magnitude
Angle(Degrees)
(d) Real
Figure 4.31:
(a) Input sequence, a unit step sequence; (b) Real part of output sequence; (c) Imaginary
part of output sequence; (d) The pole, plotted in the complex plane.
It can be seen that as
p
approaches 1.0, the steady state Unit Step response will approach infinity.
Example 4.19.
Demonstrate with several example computations that Eq. (4.20) holds true not only for
real poles, but also for complex poles having magnitude less than 1.0.
A simple method is to use the function
filter
; a suitable call for a single-pole IIR is
p = 0.9*j; y = filter([1], [1,-p], [ones(1,150)])
where
p
is the pole.
Another way is to write an expression which will convolve a unit step of significant length, say 200
samples, with a truncated version of the single-pole IIR's impulse response. A suitable call to create the
impulse response and perform the convolution might be
p = 0.9*j; xp = 0:1:99;x=p.ˆxp; y = conv(x, ones(1,200))
For either of the two methods described above, examine the output sequence to find the steady-state
value. If the magnitude of the pole is too close to 1.0, it may be necessary to use longer test sequences than
