FIR Filter Coefficient Calculation for Beam-Forming Arrays
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for calculating FIR filter coefficients for beam-forming filters in transducer arrays face challenges such as impractical designs due to frequency sampling design, time-domain aliasing, and high complexity, limiting their application to small arrays with small filter orders.
Innovation Solution
A two-stage process for calculating FIR filter coefficients, where frequency domain filter weights are first determined to achieve target frequency responses, followed by calculating time-domain coefficients to approximate these responses, allowing for independent frequency resolution and secondary condition optimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Illumination intensity
If frequency sampling design is used to determine FIR filters from inverse discrete Fourier transformation, then the frequency response can be indicated over the entire time-discrete frequency axis, but the resulting FIR filters exhibit excessive gain values at specific frequencies due to heavy fluctuations between the frequency sampling points
Solution Approach 1:
The patent applies windowing functions to the impulse responses before performing the inverse discrete Fourier transformation. This preliminary action smooths the frequency response and prevents excessive gain values at specific frequencies by reducing the fluctuations between frequency sampling points, thereby resolving the contradiction between frequency response coverage and filter stability
Solution Approach 2:
The patent introduces windowing functions as an intermediary element between the impulse responses and the frequency domain transformation. These windowing functions act as a mediator that modifies the impulse responses to produce smoother frequency responses, eliminating the harmful fluctuations while maintaining the desired frequency response coverage
2Ease of manufacture
If the length of the FIR filter is automatically determined from the resolution of the defined frequency response, then the filter design is simplified, but the filters are prone to time-domain aliasing requiring additional techniques such as zero-padding or windowing
Solution Approach 1:
The patent converts the harmful effect of time-domain aliasing into a beneficial outcome by deliberately applying windowing functions. The windowing process, while modifying the frequency response, effectively suppresses time-domain aliasing and produces more stable and reliable beam-forming filters, transforming a potential drawback into an advantage
3Adaptability or versatility
If FIR coefficients are determined directly within the time-domain in a one-stage process, then the emission behavior can be represented directly as a function of the FIR coefficients, but the optimization problem becomes extremely complex with rapidly increasing dimension proportional to the number of frequency raster points and spatial resolution
Solution Approach 1:
The patent segments the filter design process into distinct stages: first determining the frequency response characteristics, then deriving the impulse responses, and finally obtaining the FIR coefficients. This segmentation breaks down the complex optimization problem into manageable steps, reducing the overall complexity while maintaining adaptability in the time-domain design
4Illumination intensity
If no sensible definitions are provided for the frequency response in certain frequency domains (very low frequencies or high frequencies), then the frequency response can be defined over the entire spectrum, but the resulting FIR filters cannot be used due to excessive gain values and heavy fluctuations
Solution Approach 1:
The patent applies different windowing functions to different parts of the frequency spectrum. By using local quality adjustments through selective windowing, the patent maintains frequency response definitions across the entire spectrum while preventing excessive gain values and fluctuations in specific frequency domains, thereby preserving filter usability
Data Source
AI summary
The effectiveness of calculating FIR filter coefficients for beam-forming filters for transducer arrays such as arrays of microphones or loudspeakers, for example, is increased in that the calculation is performed in two stages; namely, on the one hand, by calculating frequency domain filter weights of the beam-forming filters, i.e., coefficients describing the transfer functions of the beam-forming filters within the dimension of the frequency so as to obtain target frequency responses for the beam-forming filters, so that applying the beam-forming filters to the array approximates a desired directional selectivity, and followed by calculating the FIR filter coefficients for the beam-forming filters, i.e., of coefficients describing the impulse response of the beam-forming filters within the time domain, such that the frequency responses of the FIR beam-forming filters approximate the target frequency responses in an optimum manner in accordance with defined criteria.