BÀI BÁO CÁO- THIẾT KẾ LOC SỐ

The filter design plots are given in Figure 8.2.Analog Elliptic Lowpass Filter Design Plots in P 8.2... The filter design plots are shown in Figure 8.6.c Comparison: The designed system fu

Analog Butterworth lowpass filter design: Ω p = 30 rad/s, R p = 1 dB, Ωs = 40 rad/s, As = 30 dB.

M ATLAB Script:

111

The filter design plots are given in Figure 8.2.

Analog Elliptic Lowpass Filter Design Plots in P 8.2

117

A PRIL 98

The filter design plots are given in Figure 8.4

Digital Butterworth Filter Design Plots in P 8.7

The filter design plots are shown in Figure 8.6.

(c) Comparison: The designed system function as well as the impulse response in part 6b are similar to those in part 6a except for an overall gain due to Fs = 1=T = 8000 This problem can be avoided if in the impulse invariance design method we set

h (n) = T ha (nT )

7 Problem P 8.7

Digital Butterworth Lowpass Filter Design using Impulse Invariance MATLAB script:

The filter design plots are shown in Figure 8.7.

Comparison: From Figure 8.7 we observe that the impulse response h (n) of the digital filter is a sampled version of theimpulse response ha (t ) of the analog proptotype filter as expected

M ATLAB verification using Problem P8.7:

A PRIL 98

The filter design plots are given in Figure 8.8

Digital Butterworth Filter Design Plots in P 8.8

The filter design plots are shown in Figure 8.9

Comparison: If we compare filter orders from two methods then bilinear transformation gives the lower order than

the impulse invariance method This implies that the bilinear transformation design method is a better one in all

aspects If we compare the impulse responses then we observe from Figure 8.9 that the digital impulse response is

not a sampled version of the analog impulse response as was the case in Figure 8.7

The filter design plots are shown in Figure 8.10.

Comparison: If we compare the plots of filter responses in part 9a with those in part 9b, then we observe that the

The filter design plots are shown in Figure 8.12.

(c) Comparison: If we compare the designed system function as well as the plots of system responses in part 10a and

in part 10a, then we observe that these are exactly same If we compare the impulse invariance design in Problem

6 with this one then we note that the order of the impulse invariance designed filter is one higher This implies that

the bilinear transformation design method is a better one in all aspects

11 Digital lowpass filter design using elliptic prototype

A PRIL 98The filter design plots are shown in Figure 8.13.

Digital Elliptic Filter Design Plots in P 8.14a

Log−Magnitude Response

0 Decibel 60 0 0.4 Frequency in Hz 0.6 1

Impulse Response

0.2 ha(t) 0

−0.2 0 10 30 5060 time in seconds 70 90 100

Figure 8.13: Digital elliptic lowpass filter design using the bilinear function in Problem P8.14a

The filter design plots are shown in Figure 8.14 From these two figures we observe that both functions give the same

design in which the digital filter impulse response is not a sampled version of the corresponding analog filter impulse

Figure 8.14: Digital elliptic lowpass filter design using the ellip function in Problem P8.14b

12 Digital elliptic highpass filter design using bilinear mapping

A PRIL 98

The filter frequency response plot is shown in the top row of Figure 8.15

The filter frequency response plot is shown in the bottom row of Figure 8.15 Both M ATLAB scripts and the Figure

8.15 indicate that we designed essentially the same filter

13 Digital Chebyshev-2 bandpass filter design using bilinear transformation M ATLAB script:

A PRIL 98

Digital Elliptic Filter Design Plots in P 8.17

Design using the dhpfd_bl function