Discrete-Time Adaptive Notch Filter for Complex Signal Distortion

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Solution Overview

Problem

Conventional digital notch filters are limited in their ability to filter complex noise signals, often inadvertently attenuating both the signal component and its complex conjugate, leading to signal distortion.

Innovation Solution

A discrete-time digital filter with a transfer function of H(z-1)=1+a1⁢z-1+a2⁢z-2+…+aN⁢z-N1+ρ⁢a1⁢z-1+ρ2⁢a2⁢z-2+…+ρN⁢aN⁢z-N is developed, which allows for the attenuation of complex noise signals without affecting their complex conjugates, thereby reducing distortion.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Object-affected harmful factors

If conventional digital notch filters are used to attenuate narrow-band signal components, then the filtering of unwanted tones is improved, but complex conjugate components are also attenuated causing signal distortion

Engineering Contradiction:

Improveunwanted tone attenuationVSAvoidsignal distortion

Core Design Contradiction:

Object-affected harmful factorsVSLoss of information

Solution Approach 1:

The filter uses asymmetric pole-zero placement in the z-plane where zeros are positioned at specific frequencies to be attenuated, but poles are placed only at a subset of these frequencies rather than symmetrically at all conjugate pairs. This asymmetric configuration allows selective attenuation of unwanted tones while preserving their complex conjugate components, eliminating signal distortion.

Inventive Principle:

Principle #4Asymmetry

Solution Approach 2:

The filter applies different treatment to different frequency components by placing poles and zeros at specific locations in the z-plane. Each pole-zero pair is configured locally to address specific unwanted frequencies while leaving other frequency components, including complex conjugates, unaffected. This localized frequency-specific processing resolves the contradiction between tone attenuation and distortion prevention.

Inventive Principle:

Principle #3Local quality

2Manufacturing precision

If poles are placed close to zeros in the z-plane to achieve narrow notch filtering, then the selectivity of the filter is improved, but the stability of the filter may deteriorate

Engineering Contradiction:

Improvefilter selectivityVSAvoidfilter stability

Core Design Contradiction:

Manufacturing precisionVSReliability

Solution Approach 1:

The filter places poles at only a subset of the frequencies where zeros are located, rather than placing poles at all zero locations. This partial action approach provides sufficient notch filtering selectivity at the critical frequencies while maintaining filter stability by avoiding excessive pole placements that would compromise reliability.

Inventive Principle:

Principle #16Partial or excessive action

Data Source

PatentUS12189051B2Discrete time adaptive notch filter

Publication Date: 2025.01.07 SRC INC

AI summary

A discrete-time, digital filter for notch filtering a complex digital signal, the filter having a transfer function allowing selective filtering of complex signal components. A system for receiving a modulated signal, the system including a processor for adaptively generating filter coefficients of a discrete-time, digital filter, for filtering a complex discrete-time signal, the processor configured to (i.) identify a number of signal samples in a discrete-time signal, and use the signal samples to calculate autocorrelation values sufficient to calculate the filter coefficients, (ii.) solve a system of equations, the system of equations defined by a Toeplitz matrix and a vector to determine the coefficient values, the Toeplitz matrix defined using the autocorrelation values, and the vector defined as the autocorrelation values of a white noise signal.