Stabilizing Multipole Speaker Weight Factors via Spherical Harmonics

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Conventional methods fail to reproduce a desired sound field using a multipole speaker array with multiple speakers that provide output outwardly, as they either reproduce directional characteristics only or use spherical speaker arrays, and lack a stable method to derive weight factors for superposition of multipoles.

Innovation Solution

A signal processing device and method that calculates spherical harmonics expansion coefficients, converts them into weight factors for multipole sources, calculates filter coefficients for each speaker, and convolves these coefficients into input acoustic signals to produce output acoustic signals for each speaker in a multipole speaker array.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If Pressure-Matching based approach is used to derive weight factors for multipole sources, then the sound field can be reproduced with multipole speaker array, but the solution becomes unstable due to ill-conditioned inverse problem

Engineering Contradiction:

Improvestability of weight factor calculationVSAvoidcomplexity of deriving weight factors

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent introduces spherical harmonics expansion coefficients as an intermediary to bridge the sound field and multipole sources. Instead of directly solving the unstable inverse problem between sound field and multipole weight factors, the solution expands the sound field into spherical harmonics coefficients first, then uses these coefficients to derive the multipole weight factors through a stable transformation process, thus avoiding the ill-conditioned inverse problem

Inventive Principle:

Principle #24Intermediary (Mediator)

Solution Approach 2:

The patent replaces the mechanical Pressure-Matching optimization approach with an analytical spherical harmonics expansion method. Instead of iteratively solving the inverse problem through pressure matching, the solution uses closed-form spherical harmonics expansion formulas to directly obtain the expansion coefficients, which are then transformed into multipole weight factors through a stable mathematical relationship

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If spherical speaker array is used, then directional characteristics can be reproduced through spherical harmonics, but the sound field cannot be reproduced with multipole speaker array that provides output outwardly

Engineering Contradiction:

Improvesound field reproduction capabilityVSAvoidspeaker array configuration flexibility

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent makes the spherical harmonics expansion method universally applicable to different speaker array configurations. By deriving the relationship between spherical harmonics coefficients and multipole sources in a configuration-independent manner, the solution enables sound field reproduction with various speaker arrangements including multipole speaker arrays with outwardly provided outputs, thus achieving multi-configurational versatility

Inventive Principle:

Principle #6Universality (Multi-functionality)

Solution Approach 2:

The patent changes the parameter representation from direct speaker position coordinates to spherical harmonics expansion coefficients. This parameter transformation allows the sound field reproduction to be configured for different speaker array geometries by simply adjusting the transformation relationship between coefficients and individual speaker signals, rather than reconfiguring the entire reproduction system

Inventive Principle:

Principle #35Parameter changes

3Reliability

If multipole sources are used for sound field reproduction, then directional characteristics can be controlled, but the weight factor derivation becomes unstable without orthogonal function properties

Engineering Contradiction:

Improvestability of weight factor derivationVSAvoidprecision of sound field expansion

Core Design Contradiction:

ReliabilityVSMeasurement precision

Solution Approach 1:

The patent introduces spherical harmonics expansion coefficients as an intermediary that leverages the orthogonal properties of spherical harmonics to stabilize the weight factor derivation. The orthogonal basis functions of spherical harmonics provide a stable mathematical foundation for expanding the sound field, and these coefficients serve as the stable intermediary from which multipole weight factors are derived without directly encountering the ill-conditioned inverse problem

Inventive Principle:

Principle #24Intermediary (Mediator)

Data Source

PatentUS11871211B2Signal processing apparatus, signal processing method, and signal processing program

Publication Date: 2024.01.09 NIPPON TELEGRAPH & TELEPHONE CORP

AI summary

A signal processing device 1 includes an expansion coefficient calculation unit 11 that, from an outward sound field to be reproduced, calculates a spherical harmonics expansion coefficient for reproducing the sound field; an expansion coefficient conversion unit 12 that converts the calculated spherical harmonics expansion coefficient into a weight factor for superposition of multipole sources; a filter coefficient calculation unit 13 that, from the weight factor, calculates a filter coefficient corresponding to each speaker included in a multipole speaker array, the speaker providing output outwardly; and a convolution operation unit 14 that convolves the filter coefficient corresponding to each speaker into an input acoustic signal to calculate an output acoustic signal for each speaker.