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444 Chapter 8 IIR FILTER DESIGN
4. [b,a]=ellip(N,Rp,As,wn)
This function designs an Nth-order lowpass digital elliptic filter with
the passband ripple of Rp decibels and a stopband attenuation of As
decibels. It returns the filter coefficients in length N +1 vectors b and
a. The filter order is given by (8.62), and the cutoff frequency wn is the
digital passband frequency in units of π; that is,
ω n = ω p /π
The use of this function is given in Example 8.24.
All these above functions can also be used to design other frequencyselective
filters, such as highpass and bandpass. We will discuss their
additional capabilities in Section 8.6.
There is also another set of filter functions, namely the buttord,
cheb1ord, cheb2ord, and ellipord functions, which can provide filter
order N and filter cutoff frequency ω n , given the specifications. These
functions are available in the Signal Processing toolbox. In the examples
to follow we will determine these parameters using the formulas given
earlier. We will discuss the filter-order functions in the next section.
In the following examples we will redesign the same lowpass filters
of previous examples and compare their results. The specifications of the
lowpass digital filter are
ω p =0.2π, R p =1dB
ω s =0.3π, A s =15dB
□ EXAMPLE 8.21 Digital Butterworth lowpass filter design:
>> % Digital Filter Specifications:
>> wp = 0.2*pi; %digital Passband freq in rad
>> ws = 0.3*pi; %digital Stopband freq in rad
>> Rp = 1; %Passband ripple in dB
>> As = 15; %Stopband attenuation in dB
>> % Analog Prototype Specifications:
>> T = 1; %Set T=1
>> OmegaP = (2/T)*tan(wp/2); %Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(ws/2); %Prewarp Prototype Stopband freq
>> % Analog Prototype Order Calculation:
>> N =ceil((log10((10^(Rp/10)-1)/(10^(As/10)-1)))/(2*log10(OmegaP/OmegaS)));
>> fprintf(’\n*** Butterworth Filter Order = %2.0f \n’,N)
** Butterworth Filter Order = 6
>> OmegaC = OmegaP/((10^(Rp/10)-1)^(1/(2*N))); %Analog BW prototype cutoff
>> wn = 2*atan((OmegaC*T)/2); %Digital BW cutoff freq
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