Polynomial Interpolator for Low-Complexity Asynchronous Sample Rate Conversion
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Solution Overview
Problem
Existing audio systems face challenges in asynchronous sample rate conversion, particularly when dealing with irrational or slowly changing sample rate ratios, as they require large oversampling ratios to minimize zeroth-order hold (ZOH) distortion, leading to increased memory requirements and computational complexity.
Innovation Solution
The use of a polynomial interpolator with a time-varying polyphase filter, optimized with a weighted least squares method and adaptive weight function updates, to minimize stop-band ripple and reduce computational load, allowing for efficient sample rate conversion without the need for ZOH and with improved frequency response.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If zeroth-order hold (ZOH) oversampling is used to reduce distortion, then conversion accuracy is improved, but memory requirements and computational complexity increase significantly
Solution Approach 1:
The patent changes the fundamental parameter of interpolation method from ZOH to polynomial interpolation. This allows achieving high conversion accuracy with a fixed, manageable number of filter coefficients regardless of the oversampling ratio, thereby resolving the contradiction between accuracy and complexity
Solution Approach 2:
The patent uses a fixed set of polynomial filter coefficients that can be reused indefinitely for any oversampling ratio, replacing the need for large numbers of ZOH filter coefficients that would be required for high accuracy, thus reducing memory requirements
2Reliability
If a large oversampling ratio is used with ZOH, then stop-band attenuation is improved, but the number of filter coefficients and memory usage increase
Solution Approach 1:
The patent changes the interpolation method from ZOH to polynomial interpolation, which provides excellent stop-band attenuation with a fixed number of coefficients independent of the oversampling ratio, thus resolving the contradiction between attenuation performance and coefficient quantity
3Device complexity
If polynomial interpolation is used instead of ZOH, then memory requirements are reduced, but stop-band ripple increases
Solution Approach 1:
The patent employs time-varying polyphase filter coefficients that adapt dynamically based on the instantaneous oversampling ratio and polyphase index, allowing the system to maintain excellent stop-band attenuation while using a fixed, small number of coefficients, thus resolving the contradiction between memory efficiency and attenuation performance
4Adaptability or versatility
If traditional SRC methods are used for irrational or slowly changing conversion ratios, then conversion flexibility is improved, but computational load increases
Solution Approach 1:
The patent creates a universal polynomial interpolator that can handle any oversampling ratio and conversion type (irrational, slowly changing, or fixed) using the same fixed set of coefficients and a simple time-varying polyphase structure, achieving high flexibility with minimal computational load
Data Source
AI summary
Methods for sample rate conversion are provided that use a polynomial interpolator with minimax stopband attenuation. A method for sample rate conversion of an input signal is provided that uses a time-varying polyphase filter having a discrete polyphase index m. Another method for sample rate conversion of an input signal is provided that uses a time-varying polyphase filter having a continuous polyphase index τ. In these methods, an output time index is mapped to an input sample index and the polyphase index, the polynomial coefficients of a polyphase filter are computed using the polyphase index, and the polyphase filter is applied to an input sample at the input sample index to generate the output sample at the output time index.