Quantized Filter Analysis - Introduction to Digital Signal Processing and Filter Design - page 368

k3 = [ − 0 . 4165 ]

0
1

v3 =

Now we log on to the FDA Toolbox by typing fdatool in the MATLAB com-
mand window and enter the following specifications to design the reference filter
under infinite precision . This is a lowpass, IIR, elliptic filter with sampling
frequency = 48 , 000 Hz, F pass = 9600 Hz ,F stop = 14 , 400 Hz, which correspond
to the normalized sampling frequency = 2, F pass = 0 . 4, F stop = 0 . 6, respectively.
The maximum passband attenuation is set as A p = 0 . 3 dB and the minimum stop-
band attenuation, as A s = 35 dB. When we design this filter, we find that the
minimum order of the filter is given as 4, and therefore we increase it to 5 as
the order of the filter so that we can realize the allpass networks in parallel and
compare it with the frequency response of other types of filters. With this selec-
tion, the frequency response and phase response displayed in the Analysis area
are as shown in Figure 7.4. The coefficients of the numerator and denominator
of the IIR reference filter are given below.
Numerator coefficients (normalized to render the constant coefficient of the
numerator as one) of this reference filter are

1 . 000000000000
1 . 337660698390
2 . 251235030190
2 . 251235030190

Magnitude and phase responses
Filter #1: Magnitude
Filter #1: Phase

1 0

0.8 − 80

− 160

0.6

0.4 − 240

Magnitude and Phase Response of Lowpass, Elliptic, IIR
Reference Filter of Order 5

0.2 − 320

0 0 − 400

5 10 15 20

Frequency(kHz)

Figure 7.4 Magnitude response of an IIR elliptic lowpass (reference filter) filter.