Polyphase Rate Conversion for Incommensurate Sampling Rates
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Solution Overview
Problem
Traditional rate conversion methods, including those using poly-phase filters, face challenges such as high computational complexity, inflexibility, and resource-intensive requirements, especially when dealing with incommensurate sampling rates or large least common multiples, which limits their efficiency and adaptability in applications like audio sampling rate conversions.
Innovation Solution
A flexible poly-phase filter structure that adjusts filter coefficients based on the phase index and allows for interpolation or approximation of filter coefficients, enabling efficient rate conversion across different sampling rates, including incommensurate ratios, by using linear or cubic interpolation and small fraction approximation techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional rate conversion methods using least common multiple are used, then rate conversion between different sampling rates is achieved, but computational complexity and resource requirements increase significantly
Solution Approach 1:
The patent changes the parameter of filter operation rate from the high least common multiple rate to the original sampling rate. By using polyphase filter decomposition, the filter is divided into multiple sub-filters that operate at the lower original sampling rate, significantly reducing computational complexity while maintaining rate conversion capability between different sampling rates
Solution Approach 2:
The patent segments the single high-rate filter into multiple polyphase sub-filters that operate at lower rates. Each sub-filter processes a specific phase of the input signal, and their outputs are combined to produce the final rate-converted output. This segmentation reduces the computational burden on individual filter operations
2Device complexity
If poly-phase filters are used for rate conversion, then computational load is reduced, but flexibility for variable sampling rates is limited
Solution Approach 1:
The patent introduces dynamic selection of polyphase sub-filters based on the actual sampling rate ratio. When the input and output sampling rates match the designed nominal rates, all polyphase sub-filters are used. When rates differ, the system dynamically selects and adjusts the appropriate subset of sub-filters, maintaining flexibility for variable rates while preserving the computational efficiency of polyphase decomposition
3Ease of manufacture
If fixed poly-phase filter structure is used, then implementation is simplified, but adaptability to unknown or variable sampling rates is reduced
Solution Approach 1:
The patent incorporates feedback mechanisms that monitor the actual input and output sampling rates and adjust the polyphase filter configuration accordingly. The system detects the sampling rate ratio and dynamically configures which polyphase sub-filters to activate and how to weight their outputs, enabling adaptation to unknown or variable rates while maintaining a relatively simple fixed filter structure
Data Source
AI summary
Poly-phase filters are used to offer an efficient and low complexity solution to rate conversion. However, they suffer from inflexibility and are not easily reconfigured. A novel design for rate converters employ poly-phase filters but utilize interpolation between filter coefficients to add flexibility to rate conversion. This interpolation can be implemented as an interpolation of the poly-phase filter results. Additional approximations can be made to further reduce the amount of calculations required to implement a flexible rate converter.