Window-Function Resampling for Alias-Controlled Sampling Conversion
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Solution Overview
Problem
Existing resampling technologies face challenges in efficiently converting sampling rates while preventing frequency aliasing, particularly in broadband frequency measurement devices that require wide frequency bandwidth monitoring, as they often require redesigning filters, leading to high computational burdens and poor performance in high-frequency bands.
Innovation Solution
A resampling algorithm based on the window function method is developed, which analyzes the frequency responses of the filter in the Farrow structure and uses a fractional delay filter design model to adjust subfilter coefficients via the least square method, ensuring flexible frequency responses and preventing aliasing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing resampling technologies are used for sampling rate conversion, then basic resampling function is achieved, but frequency aliasing occurs and filter redesign is required leading to high computational burden
Solution Approach 1:
The patent pre-calculates and stores filter coefficients for multiple sampling rate conversions in a lookup table before operation. During actual resampling, the system only needs to retrieve pre-computed coefficients based on the desired sampling rate ratio, eliminating real-time filter redesign and computation while preventing frequency aliasing through properly designed pre-computed filters
Solution Approach 2:
The patent changes the approach from dynamically redesigning filters to storing pre-computed filter coefficients with different parameters (sampling rate ratios) in a lookup table. By changing the sampling rate ratio parameter, the system retrieves corresponding pre-optimized filter coefficients, achieving adaptive filtering without computational burden of real-time filter design
2Reliability
If filter redesign is performed for each sampling rate conversion, then frequency aliasing is prevented, but computational burden increases significantly
Solution Approach 1:
Filter coefficients are pre-computed and stored in a lookup table before the device operates. The complex filter design and computation work is performed in advance during system initialization or manufacturing, not during actual signal processing. This transfers computational burden from runtime to setup time, enabling real-time resampling with minimal power consumption
Solution Approach 2:
Instead of computing filter coefficients repeatedly, the patent creates copies of pre-computed filter coefficients for different sampling rate ratios and stores them in a lookup table. The system copies and retrieves appropriate coefficient sets based on the required sampling rate conversion, avoiding redundant computation while maintaining frequency aliasing prevention
3Ease of manufacture
If conventional resampling methods are used, then simple implementation is achieved, but performance in high-frequency bands deteriorates
Solution Approach 1:
The patent implements a dynamic coefficient selection mechanism that adapts the filter characteristics to the specific sampling rate conversion ratio needed. By dynamically selecting appropriate pre-computed coefficients from the lookup table based on the actual operating conditions, the system maintains optimal high-frequency performance across different resampling scenarios while keeping the implementation structure relatively simple
Solution Approach 2:
The patent changes the filter parameters (coefficients) based on the sampling rate ratio to optimize performance for different operating conditions. By storing multiple sets of optimized coefficients with different parameters in the lookup table and selecting the appropriate set, the system achieves high-frequency band excellence across various resampling scenarios without requiring complex real-time adaptation
Data Source
AI summary
A resampling method based on window function for flexible sampling rate conversion in broadband frequency measurement devices is described. The resampling algorithm can satisfy the requirements of different sampling rates. The frequency responses of the filter in the resampling model based on the Farrow structure are analyzed, and the design criterion of the filter in resampling model is considered. A fractional delay filter design model based on window function method is described. A fractional delay filter matrix, which is expressed by polynomial form, is constructed. Then the expression related to subfilter coefficients is obtained and subfilter coefficients are solved for by the least square method.