Enhanced Transposed Farrow Structure for Digital Sample Rate Conversion
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Solution Overview
Problem
Existing digital sample rate conversion technologies face a trade-off between quality and computational complexity, leading to high power consumption and large footprint, especially when converting between arbitrary sample rates, as they often require either a Farrow structure for rate increases or a Transposed Farrow structure for rate decreases, which are costly and limit functionality.
Innovation Solution
The proposed solution involves an enhanced Transposed Farrow Structure that reduces computational complexity by integrating the continuous time impulse response over all values, using a piecewise polynomial function with matrix coefficients derived from lower-order Transposed Farrow structures, and incorporating an accumulate-and-load unit for efficient sample rate conversion, allowing for both rate increases and decreases with improved aliasing properties.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional sample rate conversion structures (Farrow or Transposed Farrow) are used to convert between arbitrary sample rates, then the conversion functionality is achieved, but the computational complexity increases leading to high power consumption and large footprint
Solution Approach 1:
The patent segments the continuous time impulse response into piecewise polynomial sections, where each section corresponds to a specific time interval. This segmentation allows the complex conversion operation to be divided into manageable polynomial evaluations, reducing overall computational complexity while maintaining arbitrary sample rate conversion capability.
Solution Approach 2:
The patent changes the parameter representation by using piecewise polynomial functions with pre-calculated coefficients instead of direct convolution with continuous impulse response. The coefficients are derived from the desired impulse response characteristics, transforming the problem into a series of simpler polynomial evaluations that reduce computational burden.
2Measurement precision
If higher order polynomial interpolation is used to improve conversion quality, then the signal-to-noise ratio improves, but the computational complexity and power consumption increase
Solution Approach 1:
The patent performs preliminary calculation of polynomial coefficients offline based on the desired impulse response characteristics. These pre-calculated coefficients are stored and reused during actual sample rate conversion operations, eliminating the need for repeated complex calculations and significantly reducing real-time power consumption while maintaining high conversion quality.
Solution Approach 2:
The patent uses piecewise polynomial approximation that provides sufficient precision for the application requirements without implementing the full mathematical complexity of exact continuous convolution. This partial action approach achieves the necessary signal-to-noise ratio with substantially reduced computational effort and power consumption.
3Adaptability or versatility
If conventional Farrow structure is used for rate increase or Transposed Farrow for rate decrease, then the conversion is achieved, but the device footprint and memory requirements increase
Solution Approach 1:
The patent creates a universal sample rate conversion structure based on piecewise polynomial evaluation that can handle both rate increase and rate decrease operations with a single unified architecture. This eliminates the need for separate Farrow and Transposed Farrow structures, reducing device footprint and memory requirements while maintaining arbitrary sample rate conversion capability.
Data Source
AI summary
Methods, structures and computer program products for digital sample rate conversion are presented. An input digital sample with a first frequency is converted to an output sample with a second frequency. A sample rate conversion circuit is provided which provides an enhanced transposed farrow structure that enables an optimised trade-off between noise levels and computational complexity. Each output sample is derived by convolution of a continuous time interpolation kernel with a continuous time step function representing the input sample stream. In a sample rate conversion structure, there is a trade-off between the quality and the computational complexity. The quality is defined as a ratio between the (wanted) signal power and the (unwanted) noise power. The computational complexity may be defined as the average number of arithmetic operations that are required to generate one output sample. A higher computational complexity will generally lead to a higher power consumption and larger footprint.