<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>A synthesis method for designing two-dimensional lossless finite impulse response (FIR) filters for various digital signal processing tasks is proposed. The synthesis method is based on using a 2-D embedding approach to obtain the paraunitary transfer function matrix of the lossless FIR filter. The elements of the paraunitary transfer function matrix are the transfer function of a given lossy FIR structure and the transfer functions for its complementary structures. The embedding method is used to design complementary FIR filter structures for several known lossy FIR filters. The lossless FIR filter matrix obtained in this article has a size of 3 × 1 and satisfies the paraunitary conditions. The conditions are described by a set of nonlinear equations. A modified Newton method is used to solve this set of equations. The proposed design method is used to determine the lossless structures of two-dimensional FIR filters for various digital processing tasks.</p>
</abstract>

A synthesis method for designing two-dimensional lossless finite impulse response (FIR) filters for various digital signal processing tasks is proposed. The synthesis method is based on using a 2-D embedding approach to obtain the paraunitary transfer function matrix of the lossless FIR filter. The elements of the paraunitary transfer function matrix are the transfer function of a given lossy FIR structure and the transfer functions for its complementary structures. The embedding method is used to design complementary FIR filter structures for several known lossy FIR filters. The lossless FIR filter matrix obtained in this article has a size of 3 × 1 and satisfies the paraunitary conditions. The conditions are described by a set of nonlinear equations. A modified Newton method is used to solve this set of equations. The proposed design method is used to determine the lossless structures of two-dimensional FIR filters for various digital processing tasks.

2–D Lossless FIR Filter Design Using Synthesis of the Paraunitary Transfer Function Matrix

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A synthesis method for designing two-dimensional lossless finite impulse response (FIR) filters for various digital signal processing tasks is proposed. The...

2–D Lossless FIR Filter Design Using Synthesis of the Paraunitary Transfer Function Matrix

Published Online: Dec 21, 2023

Page range: 673 - 686

Received: Dec 28, 2022

Accepted: May 26, 2023

DOI: https://doi.org/10.34768/amcs-2023-0048

Keywords
lossless system, paraunitary transfer function matrix, FIR filter, embedding method

© 2023 Krzysztof Wawryn et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

2–D Lossless FIR Filter Design Using Synthesis of the Paraunitary Transfer Function Matrix

Published Online: Dec 21, 2023

Page range: 673 - 686

Received: Dec 28, 2022

Accepted: May 26, 2023

DOI: https://doi.org/10.34768/amcs-2023-0048

Keywordslossless system, paraunitary transfer function matrix, FIR filter, embedding method

© 2023 Krzysztof Wawryn et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
lossless system, paraunitary transfer function matrix, FIR filter, embedding method