Spectrogram-Based Sampling Rate Conversion for Flexible Decimation
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Solution Overview
Problem
Current methods for decimating sampling rates in signal processing are inefficient, particularly at high relative bandwidths, leading to increased computing time, storage requirements, and complexity, with existing techniques like polyphase filters and Farrow interpolators failing to provide adequate signal quality and flexibility.
Innovation Solution
The proposed solution involves a system that modifies sampling rates through a combination of forward and reverse transformations and time domain interpolation, allowing for flexible adaptation of sampling rates with efficient polynomial interpolation, reducing computing effort and signal deviations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If polyphase filter with heavy oversampling is used for decimation, then decimation with variable sampling rate is achieved, but computing time and storage requirements increase disproportionally
Solution Approach 1:
The patent segments the decimation process into multiple stages: a first decimation stage using a polyphase filter with oversampling factor n1, followed by a second decimation stage using a different polyphase filter with oversampling factor n2. This multi-stage segmentation allows achieving high overall decimation ratios while keeping individual filter complexities manageable, thus reducing total computing time compared to a single-stage approach with equivalent total decimation.
Solution Approach 2:
The patent implements dynamic adaptability by allowing different oversampling factors (n1 and n2) and different decimation ratios (m1 and m2) in different stages, enabling the system to optimize performance for variable sampling rate requirements. The filters can be configured with different parameters depending on the specific decimation task, providing flexibility without proportionally increasing computing burden.
2Adaptability or versatility
If polyphase filter with heavy oversampling is used for decimation, then decimation with variable sampling rate is achieved, but storage requirements increase disproportionally
Solution Approach 1:
The patent divides the total decimation task into multiple stages with separate polyphase filters, each having its own impulse response stored in memory. By segmenting the decimation ratio into smaller factors (n1 and n2), the storage requirements for each filter's coefficient memory are reduced compared to storing a single large filter with equivalent total decimation ratio, thus lowering overall storage requirements while maintaining variable sampling rate capability.
3Adaptability or versatility
If Farrow interpolator is used for sampling rate modification, then interpolation is achieved, but SFDR is poor in the range of approximately 50 dB
Solution Approach 1:
The patent employs multiple decimation stages instead of a single Farrow interpolator stage. Each stage uses a polyphase filter with controlled oversampling, which provides better spectral separation and higher SFDR compared to a single-stage Farrow approach. The multi-stage segmentation allows achieving SFDR significantly better than 50 dB by progressively filtering and decimating the signal.
4Adaptability or versatility
If Farrow interpolator is used for sampling rate modification, then interpolation is achieved, but additional computing effort is required for bandwidth limitation
Solution Approach 1:
The patent merges the decimation and filtering functions into a single polyphase filter structure. The polyphase filter inherently performs both the decimation (by selecting every m-th sample) and the anti-aliasing filtering (through its impulse response convolution) in one operation. This merging eliminates the need for separate bandwidth limitation stages that would be required with Farrow interpolators, thus reducing total computing effort while maintaining sampling rate modification capability.
Data Source
AI summary
An apparatus for modifying a sampling rate includes a forward transformer for forming a first version of a spectrogram by means of transformation with a first transformation length from an information signal with a first sampling rate. The apparatus includes a processor for forming a second version of the spectrogram with a lower bandwidth than the first version. The apparatus includes a reverse transformer for forming a coarsely pre-modified information signal with a second sampling rate that is reduced with respect to the first sampling rate, by means of reverse transformation of the second version of the spectrogram with a second transformation length that is reduced with respect to the first transformation length. The apparatus includes a time domain interpolator for acquiring an information signal with a third sampling rate that is modified with respect to the second sampling rate, by means of interpolation of the pre-modified information signal.