Farrow Resampling Filter Using Lookup Tables for Fixed Sample Rates
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Solution Overview
Problem
Digital signal processing systems face challenges in efficiently converting sampled signals between incompatible sample rates, particularly when the ratio of sample rates cannot be expressed as low-order integers, leading to impractical up-conversion rates or large polyphase stages.
Innovation Solution
A Farrow-based resampling filter method that uses a lookup table to provide predetermined interpolation factors for resampling, reducing computational resources and improving accuracy by fixing and locking input and output sample rates to a common frequency reference, allowing for real-time operation with less computational overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional up-conversion or down-conversion filters are used for integer ratio sampling, then the implementation is straightforward, but the method cannot handle incompatible sample rates with non-integer ratios
Solution Approach 1:
The resampling process is segmented into multiple polyphase stages (N stages for N/M ratio), where each stage processes a portion of the signal. This allows the complex resampling operation to be divided into manageable parallel filter banks, making implementation feasible for high-resolution incompatible rate conversions.
Solution Approach 2:
The patent transitions from time-domain filtering to frequency-domain processing by using the relationship between sample rates and clock domains. By operating in the frequency domain and using spectral replication concepts, the system achieves resampling without requiring impractically complex time-domain filters.
2Adaptability or versatility
If polyphase architecture is used with high N/M ratios, then incompatible sample rate conversion is achieved, but the number of polyphase stages becomes impractically large
Solution Approach 1:
The system pre-calculates and stores resampling parameters, filter coefficients, and timing information in lookup tables before operation. This preliminary preparation allows the actual resampling process to proceed with reduced real-time computation, making high N/M ratios feasible without requiring an impractically large number of active polyphase stages.
Solution Approach 2:
A clock domain converter acts as an intermediary between the input sample clock and output sample clock domains. This mediator component handles the complex timing and rate conversion logic, allowing the polyphase filters to operate with simplified timing requirements and reducing the effective number of stages needed.
3Measurement precision
If Farrow filter with arbitrary position interpolator is used, then resampling accuracy is improved, but computational resources increase
Solution Approach 1:
Interpolation factors and filter coefficients are pre-calculated and stored in lookup tables based on the fixed N/M resampling ratio. During operation, the system retrieves these pre-computed values rather than calculating them in real-time, maintaining high resampling accuracy while dramatically reducing the computational resources required during actual signal processing.
Solution Approach 2:
The system changes the operational parameters by fixing the sample rates to be submultiples of a common system clock rate. This parameter constraint allows the use of simplified integer-based timing and indexing into lookup tables, reducing computational complexity while maintaining the accuracy benefits of arbitrary position interpolation.
Data Source
AI summary
Systems and method for resampling are provided. A method of resampling includes receiving a first sampled signal that is sampled at a first sample rate, where the first sample rate is a submultiple of a system clock rate for a Farrow filter. The method further includes resampling the first sampled signal, using the Farrow filter having a plurality of finite impulse response (FIR) filters and an arbitrary position interpolator, at a second sample rate to generate a second sampled signal. The interpolation factor for each sample of the second sampled signal is retrieved from at least one lookup table stored in memory and the first sample rate and the second sample rate are fixed and locked to a common frequency reference. The method further includes outputting the second sampled signal at the second sample rate.