Optimal Design of 2-D Recursive Digital Filters and Filter Banks based on 2-D All-pass Filters with Novel Lattice Structure
Date Issued
2014
Date
2014
Author(s)
Chen, Chun-Cheng
Abstract
Using allpass filters as basic building block to construct digital filters has the advantages of passband magnitude low sensitivity and doubly complementary property. Therefore, it has been widely used in digital filter design. Lattice form allpass filter has its entire frequency response less sensitive to round-off error. So, using lattice allpass filter as basic building block can achieve low sensitivity not only in the passband magnitude, but also in the stopband magnitude and the entire phase response. Additionally, the stability of lattice allpass filter can be easily determined by its reflection coefficients, and the structure of lattice allpass filter is highly modular. These advantages bring a lot of convenience to filter design process and hardware implementation.
So far, lattice form is mostly used in one-dimensional filters. Since direct form and lattice form have one-to-one mapping in 1-D case, the two structures can theoretically achieve the same performance. But two-dimensional polynomials are not factorizable in general. Mapping from direct form to lattice form no longer exists in 2-D case. Some 2-D lattice structures have been proposed, but most of them have the performance much worse than direct form. Only the one with symmetric half plane support region using finite impulse response polynomials as its reflection coefficients can achieve the performance close to direct form.
In fact, 2-D lattice form has several different patterns. We propose a generalized 2-D lattice structure, which formats and parameterizes all possible variations of 2-D lattice forms. By adjusting the structural parameters, we can arbitrarily generate new lattice structures. For a specific filter design problem, we try several kinds of lattice structures. Computer simulations show that on the design of general 2-D filters, 2-D doubly complementary filter pairs, and 2-D quadrature mirror filters, there exists some lattice structures which can provide the design performance very close to or even better than direct form.
We also improve the optimization algorithm and objective function used in our experiment. Computer simulations show that the improved algorithm and objective function really enhance the design performance and reduce the required computation time.
Subjects
晶格架構
全通濾波器
非線性最佳化問題
二維濾波器
雙重互補濾波器對
正交鏡像濾波器組
多速率系統
Type
thesis
File(s)![Thumbnail Image]()
Loading...
Name
ntu-103-R01942072-1.pdf
Size
23.32 KB
Format
Adobe PDF
Checksum
(MD5):ddeacdb1908715778141f3b4e81380c5