Proportional Bandwidth Filter System for Multi-Octave Signal Analysis
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Solution Overview
Problem
Current spectrum analyzers are inadequate for analyzing signals with proportional bandwidths, particularly for non-stationary signals and those spanning multiple decades, as they lack the necessary flexibility and dynamic range to effectively track harmonics and frequency changes.
Innovation Solution
A proportional bandwidth filter system comprising a bandwidth reducing filter, down-sampler, and octave filters, which includes a finite impulse response (FIR) half-band filter for 2-1 bandwidth reduction and 2-1 down-sampling, along with multiple sets of proportional bandwidth filters, supports a wide dynamic range and logarithmic frequency scaling to analyze signals across multiple octaves.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If standard equal bandwidth spectrum analyzers are used, then the analysis is simple and straightforward, but they cannot effectively track harmonics that move unequal intervals and fail to analyze signals with proportional bandwidths
Solution Approach 1:
The spectrum analysis function is segmented into multiple octave bands (first octave, second octave, etc.), with each octave further divided into proportional bandwidth filters. This segmentation allows the system to handle different frequency ranges with appropriate filter characteristics, enabling effective tracking of harmonics across multiple decades while maintaining manageable complexity through modular processing.
Solution Approach 2:
The system dynamically adjusts filter bandwidths to be proportional to center frequencies rather than fixed. The bandwidth reducing filter and down-sampler dynamically process signals to maintain constant Q characteristics across octaves, allowing the analyzer to adapt to the proportional bandwidth requirements of audio and vibration signals while managing computational complexity through efficient signal processing.
2Measurement precision
If proportional bandwidth filters are used for audio and vibration analysis, then the analysis accuracy for harmonics is improved, but the computational workload increases
Solution Approach 1:
The frequency spectrum is segmented into octave portions, with each octave processed by dedicated proportional bandwidth filters. This segmentation allows precise harmonic tracking within each octave while distributing computational workload across multiple processing stages, preventing any single stage from becoming a computational bottleneck.
Solution Approach 2:
The bandwidth reducing filter performs preliminary processing by reducing the bandwidth of the input signal before it enters the proportional bandwidth filter stages. The down-sampler further prepares the signal by rolling the second octave portion to the top octave portion. These preliminary actions reduce the computational burden on subsequent filtering stages while preserving the precision needed for harmonic tracking.
3Adaptability or versatility
If the spectral range is extended to cover multiple decades, then the versatility of the analyzer is improved, but the difficulty of detecting and measuring increases
Solution Approach 1:
The wide spectral range covering multiple decades is segmented into multiple octave bands (first octave, second octave, etc.). Each octave is processed by dedicated proportional bandwidth filters, making the measurement of wideband signals manageable by breaking down the complex task into simpler, frequency-specific processing stages.
Solution Approach 2:
The system uses a multi-octave architecture that adds a dimensional approach to frequency analysis. By organizing filters across multiple octaves with proportional bandwidth characteristics, the system effectively extends the spectral range while maintaining constant Q properties, transforming the challenge of wideband analysis into a structured multi-dimensional processing approach.
Data Source
AI summary
A system and method for filtering an input signal with at least a first and a second octave portions is presented. A proportional bandwidth filter system includes a bandwidth reducing filter, a down-sampler, and first and second octave filters. The bandwidth reducing filter reduces the bandwidth of the input signal and the down-sampler rolls the second octave portion represented in the reduced bandwidth signal to a top octave portion of a down-sampled signal. The first and second octave filters are comprised of a plurality of proportional bandwidth filters. The first octave filter partitions and converts the first octave portion of the input signal into output signals representing the frequency spectra of the first octave of the input signal. Similarly, the second octave filter generates outputs representing the spectra of the second octave portion of the input signal represented as the top octave portion of a down-sampled signal.