Sampling Rate Conversion Using Factorized Time-Varying Filters
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Solution Overview
Problem
Existing sampling rate conversion methods face challenges in efficiently handling arbitrary and time-varying sampling rates, particularly when input and output sampling rates are related by an arbitrary factor that can change over time, leading to high computational complexity and memory requirements.
Innovation Solution
A method and apparatus for non-uniform sampling rate conversion that factorizes the time-varying filter into two parts, one dependent on output sampling instants and the other on input instants, allowing for recursive computation and low memory requirements, especially suitable for filters with exponential impulse responses.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If arbitrary sampling rate conversion is performed using time-varying discrete-time filter with large number of samples stored, then conversion accuracy is improved, but memory requirements increase
Solution Approach 1:
The patent segments the time-varying filter into multiple sub-filters with different impulse response lengths. Longer sub-filters capture more signal history for accurate conversion, while shorter sub-filters reduce memory requirements. The output is formed by combining results from these segmented filters, achieving balance between accuracy and memory efficiency.
Solution Approach 2:
The patent dynamically adjusts the number and length of sub-filters based on the instantaneous sampling rate ratio. When the sampling rate ratio changes abruptly, the system adapts by modifying which sub-filters are active and their respective weights, allowing accurate tracking of time-varying rates without storing all possible filter configurations in memory.
2Measurement precision
If arbitrary sampling rate conversion is performed using sophisticated interpolation techniques, then conversion accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent divides the conversion process into multiple parallel sub-filter operations rather than using a single complex interpolation algorithm. Each sub-filter uses a simpler computation scheme, but their combined output achieves high conversion accuracy, reducing overall computational complexity while maintaining precision.
Solution Approach 2:
The patent uses a finite number of sub-filters with predetermined impulse response lengths, applying partial action principle. Instead of computing an infinite impulse response or using overly sophisticated interpolation, the system uses a sufficient but limited set of sub-filters that provide adequate accuracy without excessive computational burden.
3Productivity
If synchronous sampling rate conversion with fixed rational factor is used, then computational efficiency is improved, but adaptability to time-varying rates deteriorates
Solution Approach 1:
The patent transforms the static synchronous conversion system into a dynamic one by introducing time-varying weights for multiple sub-filters. The system maintains the computational efficiency of fixed-rate conversion structures while adapting to time-varying sampling rates through dynamic weight adjustment, achieving both efficiency and adaptability.
Solution Approach 2:
The patent creates a universal conversion apparatus that can handle both fixed rational rate conversions and arbitrary time-varying rate conversions using the same sub-filter bank structure. By configuring different weights and activating different sub-filters, the system performs multiple conversion functions without requiring separate dedicated structures for each case.
4Measurement precision
If up-sampling and down-sampling by large integer factors is used, then conversion accuracy is improved, but computational requirements increase
Solution Approach 1:
The patent segments the large up-sampling and down-sampling operations into multiple smaller stages implemented through parallel sub-filters. Instead of performing one large integer-factor conversion that requires high computational power, the system distributes the work across multiple sub-filters with smaller effective factors, reducing peak computational requirements while maintaining accuracy.
Data Source
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AI summary
A signal conversion from an input signal to an output signal where the filter used is factorized so that the conversion comprises determining 1) only a first factor at each sampling time of the input signal, where this first factor is independent on the sampling times of the output signal, and 2) only a second factor at each sampling time of the output signal, where this second factor is independent of the sampling times of the input signal. This reduces the computational load for this conversion. In addition, for most filters, the factors may be calculated recursively further increasing the computational load and also reducing the storage requirements. This allows for instantaneous changes in the sampling rates or non-uniform sampling rates with low computational requirements and low memory usage.