Newton Polyphase Filters for High-Attenuation Interpolation
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Solution Overview
Problem
Current polyphase filter configurations face a trade-off between filter performance and the number of filter coefficients, where increased filter length requires more bits for coefficient representation, leading to high side-lobes and degraded stop-band attenuation if insufficient bits are allocated.
Innovation Solution
The implementation of a cascade of template filters with identical transfer functions, combined and interleaved to produce polyphase outputs, reducing computational complexity and coefficient dynamic range, and replacing multiplication operations with shift and add operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the filter length is increased to improve stop-band attenuation, then the filter performance is improved, but the number of bits required to represent coefficients increases, leading to higher complexity and quantization requirements
Solution Approach 1:
The filter is divided into multiple polyphase components (e.g., H0(z), H1(z), H2(z), H3(z)) that operate at lower sampling rates. Each phase processes a subset of the input samples, allowing the overall filter to achieve high stop-band attenuation while each individual phase uses fewer coefficients with lower precision requirements.
Solution Approach 2:
The filter design transitions from a single high-order filter operating at the full sampling rate to multiple lower-order filters operating in parallel at decimated sampling rates. This dimensional transformation in the polyphase domain allows achieving the same attenuation performance with reduced coefficient complexity in each branch.
2Manufacturing precision
If more bits are allocated to represent filter coefficients, then the filter performance and stop-band attenuation are improved, but the computational complexity and resource requirements increase
Solution Approach 1:
By segmenting the filter into polyphase components, each processing a fraction of the total signal, the required precision for each segment's coefficients is reduced. The segmentation allows using fewer bits per coefficient while maintaining overall filter performance through the combined effect of all phases.
Solution Approach 2:
The invention changes the operating parameters of the filter by using different sampling rates for different polyphase branches. This parameter change allows each branch to use lower-precision coefficients appropriate for its reduced sampling rate, while the overall system achieves high precision through coherent combination of all branches.
3Manufacturing precision
If a single high-order filter is used to achieve high interpolation factors, then the filter performance is improved, but the computational complexity at the full sampling rate increases significantly
Solution Approach 1:
The high-order filter is segmented into multiple lower-order polyphase filters that operate in parallel. Each polyphase filter processes samples at a decimated rate, reducing the computational load per unit time. The segmentation distributes the computational complexity across multiple simpler units rather than concentrating it in a single high-order filter.
Solution Approach 2:
The polyphase decomposition performs preliminary filtering operations at reduced sampling rates before combining the results to achieve the final high-rate output. This preliminary action at lower rates reduces the overall computational complexity compared to performing all operations at the full sampling rate.
Data Source
AI summary
An interpolation filter for interpolating a digital signal includes a cascade of template filters, each having an identical template transfer function A(z), which is arranged to receive and filter an input sequence representing the digital signal sampled at an input sampling rate. Ancillary circuitry is coupled to the cascade so as to produce first and second phase outputs. A multiplexer is arranged to multiplex the phase outputs in order to generate an output sequence having an output sampling rate equal to twice the input sampling rate.