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Advisor : Yung-An Kao Student : Chih-Wei Chen 2006/05/05 PowerPoint Presentation
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Eigenfilters: A New Approach to Least-Squares FIR Filter Design and Applications Including Nyquist Filters. Advisor : Yung-An Kao Student : Chih-Wei Chen 2006/05/05. IEEE Transaction on circuits and system, vol. CAS-34, NO. 1, January 1987

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slide1

Eigenfilters: A New Approach to Least-SquaresFIR Filter Design and ApplicationsIncluding Nyquist Filters

Advisor : Yung-An Kao

Student : Chih-Wei Chen

2006/05/05

slide2
IEEE Transaction on circuits and system, vol. CAS-34, NO. 1, January 1987
  • P.P. VAIDYANATHAN, and TRUONG Q. NGUYEN
outline
Outline
  • Introduction
  • Linear phase FIR Low-Pass eigenfilters
  • Example
introduction
Introduction
  • A new method of designing linear-phase FIR filter is proposed, the method is based on the computation of an appropriate real, symmetric, and positive-definite matrix.
  • The proposed design procedure is general enough to incorporate both time and frequency domain constraints
  • Application
  • Nyquist filter
  • Equiripple filter
introduction1
Introduction
  • The desired response is
  • The amplitude response of H(z) is

Type I filter

introduction2
Introduction
  • The least-squares (LS) approach
  • Linear equation , LSE solution can be express matrix from
linear phase fir low pass eigenfilters
Linear phase FIR Low-Pass eigenfilters
  • We wish minimizing an error measure using another method
  • If error measure can be expressed the from
linear phase fir low pass eigenfilters1
Linear phase FIR Low-Pass eigenfilters
  • The FIR linear phase filter frequency response

Type I filter

Type II filter

linear phase fir low pass eigenfilters4
Linear phase FIR Low-Pass eigenfilters
  • Passband error

It cannot be written in the form

Change, derive zero-frequency response is given by

linear phase fir low pass eigenfilters6
Linear phase FIR Low-Pass eigenfilters
  • Total measure to be minimized is
linear phase fir low pass eigenfilters8
Linear phase FIR Low-Pass eigenfilters
  • The solution
  • Step1:Given ωp、 ωs、αcomputeP
  • Step2: Compute the eigenvalue and eigenvector of P
  • Step3: Find smallest eigenvalue corresponding eigenvector