SSM Signal Encoding Using Z-Transform Segmentation
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Solution Overview
Problem
Conventional methods for encoding and decoding data inputs in SSM models face limitations in computational complexity, sequence length, discrete vs. continuous signal operation, and robustness to noise, particularly in applications like pattern recognition and robotics.
Innovation Solution
A biologically-inspired representation and algorithms that generalize SSM models to work with weighted sequences, using z-transform and Laplace transform for discrete and continuous signals, enabling efficient encoding and decoding across arbitrary sequence lengths and noise robustness, with the ZUV and SUV families of algorithms for discrete and continuous spike trains respectively.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional SSM encoding methods are used, then encoding can be performed, but computational complexity increases and sequence length is limited
Solution Approach 1:
The patent segments the encoding process into discrete time steps where only a limited number of previous states need to be stored and processed. By dividing the sequence processing into manageable segments (time steps with finite memory depth), the system achieves efficient encoding without requiring complex computation across the entire sequence at once.
Solution Approach 2:
The patent introduces transform parameters (z-transform for discrete time, Laplace transform for continuous time) that convert the encoding problem into a domain where simpler operations can be performed. These parameter transformations allow the system to handle arbitrary sequence lengths efficiently by converting complex temporal dependencies into algebraic operations in the transform domain.
2Reliability
If conventional methods are used for discrete signals, then encoding works for discrete data, but robustness to noise is insufficient
Solution Approach 1:
The patent creates a unified SSM framework that handles both discrete-time and continuous-time signals through a single theoretical structure. By using transform methods (z-transform and Laplace transform) that can process both discrete and continuous domains, the system achieves universality and can robustly handle noise in either signal type without requiring separate specialized methods.
Solution Approach 2:
The patent introduces transform domains (z-domain for discrete, s-domain for continuous) as intermediaries between the input signals and the encoding process. These transform domains act as mediators that filter out noise and simplify the encoding operation, allowing robust encoding of noisy signals by working in a transformed representation rather than directly in the time domain.
3Adaptability or versatility
If SSM models are extended to weighted sequences, then sequence length can be arbitrary, but algorithm complexity increases
Solution Approach 1:
The patent replaces mechanical sequence processing (iterating through each element and maintaining full history) with mathematical transform operations. By substituting the mechanical approach of processing every previous element with algebraic transform operations, the system achieves arbitrary sequence length handling with reduced algorithmic complexity.
Solution Approach 2:
The patent transforms the encoding problem from the time domain to the transform domain (z-domain or s-domain). This dimensional change allows the system to handle sequences of arbitrary length by converting temporal dependencies into algebraic operations in the transformed domain, where the complexity is managed through the transform parameters rather than through lengthy sequential processing.
Data Source
AI summary
Disclosed herein are embodiments of methods for encoding, decoding, and matching patterns in collections of signals. These methods use weighting functions to scale the signals. This scaling enables the use of signals of arbitrary duration, wherein the signals may include discrete sequences and spike trains. In the most general case, the signals can be represented using functionals, which extends the expressive power of the methods. Further disclosed herein are embodiments of a system that performs these methods.