Design of iir notch filters and narrow and wide band filters

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http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559
Design of IIR Notch Filters and Narrow and Wide-Band Filters
Institute of Electrical and Electronics
Engineering
Abstract:
In this thesis, a direct IIR design method for real WDFs based on Gazsi's work is summarized in detail,
and the cascade realization of first- and second-order all pass sections is generalized to any IIR transfer
function, and then a simple design method for bi-reciprocal lattice WDFs is given. A design and
realization method for IIR multiple notch filters based on the phase of an all pass filter approximation is
described. A design and realization method for high speed narrow-band and wide-band WDFs based on
the IFIR technique is given, both nonlinear and approximately linear phase filters are considered; the
narrow band filter is composed of a model filter and one or several masking filters in cascade. In the
case of nonlinear phase, conventional lattice and bi-reciprocal lattice WDFs are used for the model and
masking filters; the overall narrow-band filter can be designed by separately designing the model and
masking filters. The wide-band filter is composed of a narrow- band filter in parallel with a series of all
pass filters, to obtain an overall wide-band filter. The narrow-band filter is designed first, and is then
connected in parallel with one of the all pass filters of the narrow-band filter. In the case of
approximately linear phase, the linear phase IIR filter is used for the model filter, and a maximum flat
linear phase FIR filter is used for the masking filter. Several advantages of these filters over directly
designed filters are that they have a substantially higher maximal sample frequency, lower round off
noise and lower finite word length. Several design examples are given to demonstrate the properties of
these filters.

(a) Single-flow Diagram of Lattice Structure
(b) Simplified Wave-flow Diagram

(c) Direct Connection of Two Ports
(d) Wave-flow Diagrams of i
th
Second-degree all pass Section

(e) Block Diagram of the Lattice WDF with Cascaded all pass Sections for order N1 (as the top
structure) and N2 (as the bottom Structure), Order of Filter, N = N1 + N2

(f) Realization Structure of bi-reciprocal Filter of Order N.
(g) Notch Filter

(a) Lattice Realization of Real Coefficients of All pass Filter
(b) Details of the Building Blocks
(h) Block Diagram of Narrow-band Filter
(i) First Order all pass Section

(j) Second Order all pass Section
(k) Structure of IIR Narrow-band Filter
(l) Structure of IIR Wide-band Filter

(m) Simplified Structure of IIR Wide-band Filter
(n) Structure of IIR Wide-band High-pass Filter

A: - Multiple Notch Filter Designs
(a) Phase Response of All pass IIR Multiple Notch Filter

(b) Unit Sample of IIR Multiple Notch Filter

(c) Magnitude Response of IIR Multiple Notch Filter

(d) Phase Response of IIR Multiple Notch Filter

B: - Wide-Band Filter Designs
(a) Impulse Response of Wide-Band Filter

(b) Magnitude Response of Overall Wide-Band Filter

(c) Attenuation Reponses of Overall Wide-band Filter

(d) Attenuation of Overall Wide-Band Filter (After zooming)

Conclusion:
In this thesis, a method to design IIR multiple notch filters for a prescribed notch frequencies and 3 dB
reflection bandwidths is discussed. This notch filter can be realized by a computationally efficient lattice
structure with very low sensitivity. An example has been given IO demonstrate the design procedure.
In the second part of this thesis, the design and realization methods for high speed narrow-band and wide-
band filters have been given, the narrow-band filters are imposed of a model filter and one or several
masking filters in cascade. In the case of nonlinear phase, Lattice and bi-reciprocal lattice WDFs are used
for the model and masking fitters; a conventional lattice WDF design method is given, a design method for
bi-reciprocal WDFs is also given in detail. The wide-band filters consist of a narrow-band filter in parallel
with one of the all pass filters. The overall narrow-band filters can be designed by separately designing the
model filter and masking filters. The overall wide-band filters can be designed by first designing a narrow-
band filter, then, by connecting is filter in parallel with an all pass filter consisting of a cascade of branches
one from each sub filter of the narrow-band filter. Estimations were given for the pass band and stop band
ripples of the individual 6iters in the narrow-band filter in order to meet the requirements for the overall
wide-band filter. This offers simple design procedures for both narrow-band and wide-band filters since a
conventional lattice WDF design method can be used. However, for many wide-band cases, these designs
imply an unnecessarily high computational complexity, because the derived estimations are based on a
worst case assumption. For the case of approximately linear phase, an approximately linear phase IR filter
is used for the mode1 filter, and MF linear phase FIR filters are used for the masking filters. Because both
cases (hem and nonlinear phase) are based on the interpolated technique, ail recursive loops contain a
number of delay elements, resulting in filters with higher maximal sample sequences compared to the
directly designed filters. We gave several examples to demonstrate the effects of quantization; the
resulting filters have lower word-lengths compared with directly designed filters. We also discussed the
round off noise and concluded that these filters are likely to be in favour.

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