Sample Rate Conversion Using Power-of-2 Upsampling Factors
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Solution Overview
Problem
Existing methods for converting sampled data from one sampling rate to another are complex and resource-intensive, especially when the sampling rate ratio is subject to variability, requiring a wide range of upsampling and downsampling factors and multiple filter coefficients.
Innovation Solution
A method that constrains the upsampling factor to be an integer power of a predetermined value, deriving filter coefficients from a reference set using linear interpolation or decimation, and iteratively determining upsampling and downsampling factors to achieve a target sampling rate within a predetermined resynchronization error factor.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a wide range of upsampling and downsampling factors are used to accommodate variability in sampling rate ratios, then the system can handle a broader range of sampling rate deviations, but the system complexity increases significantly
Solution Approach 1:
The patent changes the parameter of upsampling factors from arbitrary integer values to powers of a predetermined integer (typically powers of 2). This parameter transformation allows the system to maintain adaptability to sampling rate variability while significantly reducing complexity, as filter coefficients for power-of-2 upsampling factors can be derived from a reference set using simple decimation operations rather than requiring completely different coefficient sets for each factor.
Solution Approach 2:
The patent segments the range of possible upsampling factors into discrete power-of-2 levels (e.g., 1, 2, 4, 8, 16...). This segmentation reduces the continuous range of possible factors into a manageable discrete set, where each segment level can be handled by deriving filter coefficients from a reference set through systematic decimation, thereby reducing overall system complexity while maintaining coverage of the required variability range.
2Measurement precision
If different filter coefficients are used for each combination of upsampling and downsampling factors, then the sampling rate conversion accuracy is maintained, but the memory resource requirement increases
Solution Approach 1:
The patent makes a single reference set of filter coefficients serve multiple functions by using it as the basis for generating filter coefficients for various upsampling factors. Instead of storing separate coefficient sets for each upsampling factor, the reference set is reused and systematically decimated to produce coefficients for different power-of-2 upsampling levels, thereby reducing memory requirements while maintaining conversion accuracy.
Solution Approach 2:
The patent performs preliminary computation and storage of a single reference set of filter coefficients at design time or initialization, which then serves as the foundation for all subsequent upsampling operations. This preliminary action eliminates the need to store multiple complete coefficient sets, as the reference set can be algorithmically transformed into the needed coefficients through decimation operations during runtime.
3Device complexity
If the upsampling factor is constrained to be an integer power of a predetermined value, then the system complexity and memory requirements are reduced, but the flexibility in achieving exact target sampling rates is limited
Solution Approach 1:
The patent introduces dynamic adjustment mechanisms that work within the constrained power-of-2 upsampling framework. By dynamically selecting appropriate combinations of upsampling and downsampling factors and adjusting filter coefficients through decimation of the reference set, the system adaptively achieves the closest possible approximation to the target sampling rate while maintaining the computational simplicity of power-of-2 operations.
Data Source
AI summary
Disclosed herein is a method and apparatus for converting a stream of samples at a first sampling rate to a stream of samples at a second sampling rate. An exemplary method includes measuring the first sampling rate; determining a first upsampling factor from a basis including: the measured first sampling rate, the target value of the second sampling rate, and a resynchronisation error factor, the first upsampling factor being constrained to be an integer power of a predetermined integer value; and deriving, from a reference set of filter coefficients and from a ratio of the first upsampling factor to a reference upsampling factor, a first set of filter coefficients for use in a first interpolation filter, the reference set of filter coefficients being for a reference upsampling factor that is an integer power of the predetermined integer value.