Abstract
The authors present a novel design algorithm for 3-D orthogonal filters. Both separable and non-separable cases are discussed. In the separable case, the synthesis leads to a cascade connection of 1-D systems. In the latter case, one obtains 2-D systems followed by a 1-D one. Realization techniques for these systems are presented which utilize Givens rotations and delay elements. The results are illustrated by examples of separable and non-separable 3-D system designs, i.e., Gaussian and Laplacian filters.
Highlights
Since the first pulse-code modulation transmission of digitally quantized speech, in World War II, digital signal processing (DSP) began to proliferate to all areas of human life
A classic DSP is based on linear systems described by impulse response functions and transfer functions implemented by structures built from adders, multipliers, and unit delays
The most common approach to orthogonal filter synthesis is a transfer function decomposition and the state space approach. When it comes to multidimensional DSP, the former technique is of a limited use due to the n-D polynomials
Summary
Since the first pulse-code modulation transmission of digitally quantized speech, in World War II, digital signal processing (DSP) began to proliferate to all areas of human life. A classic DSP is based on linear systems described by impulse response functions and transfer functions implemented by structures built from adders, multipliers, and unit delays. Another approach was initiated by [31], known as the state space approach. The most common approach to orthogonal filter synthesis is a transfer function decomposition and the state space approach When it comes to multidimensional DSP, the former technique is of a limited use due to the n-D polynomials. When one improves one parameter, another gets worse This can readily be seen when comparing direct form structures of infinite impulse response 1-D digital filter (fast and inaccurate) and cascade ones (more accurate but output is delayed) for high orders.
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