Constrained least squares design of 2-D FIR filters

• Published in: IEEE transactions on signal processing Vol. 44; no. 5; pp. 1234 - 1241
• Main Authors: Lang, M., Selesnick, I.W., Burrus, C.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.1996; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Chebyshev approximation; Convergence of numerical methods; Design methodology; Detection, estimation, filtering, equalization, prediction; Eigenvalues and eigenfunctions; Equations; Exact sciences and technology; Finite impulse response filter; Frequency; IIR filters; Information, signal and communications theory; Least squares methods; Nonlinear filters; Signal and communications theory; Signal, noise; Telecommunications and information theory; Lagrange multiplier; Two dimensional filtering; Linear phase; Finite impulse response filter; Frequency domain method; Kuhn Tucker condition; Mean square error
• ISSN: 1053-587X
• DOI: 10.1109/78.502335

We consider the design of 2-D linear phase finite impulse response (FIR) filters according to the least squares (LS) error criterion subject to equality and/or inequality constraints. Since we use a frequency domain formulation, these constraints can be used to explicitly prescribe (frequency-dependent) error tolerances, the maximum, minimum, or fixed values of the frequency response at certain points and/or regions. Our method combines Lagrange multiplier and Kuhn-Tucker theory to solve a much wider class of problems than do standard methods. It allows arbitrary compromises between the LS and the equiripple design.