Window-Function Resampling for Arbitrary Sampling Rate Conversion
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Solution Overview
Problem
Existing resampling technologies face limitations in flexibility and computational burden, particularly in designing filters for arbitrary sampling rate conversion, and fail to effectively prevent frequency aliasing and meet the requirements of broadband frequency measurement devices.
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
1Adaptability or versatility
If existing resampling technologies are used, then sampling rate conversion can be achieved, but flexibility in adjusting frequency responses is limited and computational burden increases
Solution Approach 1:
The filter is divided into multiple subfilters with different characteristics. Each subfilter handles a specific frequency range or function, allowing independent optimization and adjustment. This segmentation enables flexible frequency response control while reducing the computational complexity of each individual subfilter compared to a single complex filter.
Solution Approach 2:
The resampling system dynamically adjusts the frequency responses of subfilters based on the specific sampling rate conversion requirements. By making the filter characteristics adaptive and changeable rather than fixed, the system achieves flexibility in handling different sampling rate scenarios without requiring excessive computational resources for each case.
2Reliability
If existing filter design methods are used, then resampling can be performed, but frequency aliasing cannot be effectively prevented
Solution Approach 1:
The system preemptively applies anti-aliasing measures by designing subfilters with specific frequency characteristics before the resampling operation. The frequency responses of subfilters are pre-adjusted to ensure that aliasing components are suppressed before they can contaminate the signal, thereby preventing frequency aliasing in advance rather than correcting it afterward.
Solution Approach 2:
Multiple subfilters act as intermediary elements between the input signal and the final resampled output. These subfilters mediate the frequency transformation process, with each subfilter handling specific frequency components and working together to achieve overall anti-aliasing效果 while simplifying the overall design process.
3Adaptability or versatility
If fixed filter designs are used, then implementation is simpler, but the filter cannot adapt to different sampling rates and delays
Solution Approach 1:
The set of subfilters is designed to serve multiple functions and multiple sampling rate conversion scenarios. By creating a universal subfilter bank that can be configured for different sampling rates and delays, the system achieves adaptability without requiring separate dedicated filters for each scenario, thereby managing design complexity while maintaining versatility.
Solution Approach 2:
The system achieves adaptability to different sampling rates and delays by changing the parameters (frequency responses) of the subfilters rather than changing the fundamental filter structure. This parameter-based adaptation allows the same subfilter framework to handle various sampling rate conversions by simply adjusting frequency response parameters, reducing overall design complexity.
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.