Arbitrary Ratio Sample Rate Conversion via Modular Arithmetic
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Solution Overview
Problem
Conventional digital sample rate conversion methods are either computationally slow or complex, particularly when dealing with non-integral scaling ratios, and require high-quality low-pass filtering to prevent aliasing, which complicates real-time processing at video rates.
Innovation Solution
A novel algorithm using only addition and subtraction with a single precomputed division for digital sample rate conversion, allowing for real-time processing at video rates by calculating interpolation coefficients through modular arithmetic, eliminating the need for complex division operations in each step.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional linear interpolation method is used, then output quality is relatively high, but computational speed is slow due to division operations required in each step
Solution Approach 1:
The invention precomputes the interpolation coefficients (m mod n and n mod m) before the actual interpolation process. By calculating these coefficients once in advance rather than performing division operations during each interpolation step, the system achieves both high output quality and improved computational speed suitable for real-time video processing
Solution Approach 2:
The invention replaces the conventional division-based interpolation calculation with a substitution using precomputed coefficients and simpler arithmetic operations. Instead of performing division operations during real-time processing, the system uses precalculated values with addition and multiplication operations, significantly reducing computational complexity while maintaining interpolation accuracy
2Measurement precision
If interpolation/decimation method is used to achieve arbitrary scaling ratios, then output quality is excellent, but device complexity and computational intensity increase significantly
Solution Approach 1:
The invention extracts and isolates the complex division operation into a separate precomputation step, removing it from the main real-time processing loop. By separating the coefficient calculation from the interpolation execution, the system achieves arbitrary scaling ratios with excellent output quality while reducing the complexity of the main processing path to simple arithmetic operations
Solution Approach 2:
The invention performs the complex modular arithmetic calculations in advance to determine the interpolation coefficients. By preparing these coefficients before the actual scaling operation, the system eliminates the need for complex division operations during real-time processing, thereby reducing device complexity while maintaining the ability to handle arbitrary scaling ratios
3Ease of manufacture
If simple down-sampling or 0-th holding is used, then implementation is simple, but scaling flexibility is limited to integral ratios only
Solution Approach 1:
The invention creates a universal interpolation algorithm that can handle both down-sampling and up-sampling operations with arbitrary scaling ratios. By using precomputed coefficients based on modular arithmetic, the same algorithmic structure adapts to different scaling scenarios (scaling down, scaling up, and non-integral ratios) without requiring separate processing paths, thus achieving both simplicity and versatility
Data Source
AI summary
A simple to implement sample rate conversion system consisting of an input/output data flow controller, interpolation coefficient generation, and output data flow control to generate the converted data stream. Sample rate conversion may be done at real time video rates, without restrictions on the conversion ratios.