Polyphase Sample Rate Conversion Using Symmetric Subfilters
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Solution Overview
Problem
Existing digital sample rate conversion techniques, such as polyphase realizations, fail to fully exploit the symmetry or anti-symmetry of impulse responses, leading to suboptimal reduction in the number of multiplications required for integer factor sample rate conversion.
Innovation Solution
A circuit that combines the benefits of symmetrical or anti-symmetrical impulse responses with polyphase realizations by using subfilters with complementary polyphase components, reducing the number of multiplications through a specific matrix transformation and diagonalization, resulting in a more efficient sample rate conversion process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional polyphase realizations are used for sample rate conversion, then the conversion can be performed at lower rates, but the symmetry or anti-symmetry of the impulse response is not fully exploited, resulting in more multiplications than necessary
Solution Approach 1:
The impulse response h(k) is segmented into L polyphase components hλ(n·LTƒ) where λ=0,...,L-1. Each polyphase component is processed separately through dedicated subfilters, allowing the overall filter to be decomposed into parallel processing paths that operate at lower rates while preserving the ability to exploit symmetry properties within each phase
Solution Approach 2:
The patent exploits the symmetry or anti-symmetry properties of the impulse response by identifying complementary polyphase components. For each phase Hλ(z), a complementary phase Hκ(z) is found such that their sum or difference yields a symmetric or anti-symmetric response. This allows reduction of multiplications by factor of 2 within each polyphase branch, as symmetric/anti-symmetric filters require only (P+1)/2 multiplications instead of P+1
2Device complexity
If symmetry or anti-symmetry of impulse response is exploited, then the number of multiplications is reduced, but traditional polyphase realizations cannot maintain both the symmetry benefit and the low-rate processing benefit simultaneously
Solution Approach 1:
The patent merges the advantages of polyphase decomposition with symmetry exploitation by combining complementary polyphase components. Specifically, for each pair of complementary phases (Hλ(z), Hκ(z)), the patent creates subfilters that process these phases together, allowing the system to achieve both low-rate processing (from polyphase) and reduced multiplications (from symmetry). The combining operation Gλ(z) = Hλ(z) + Hκ(z) or Gλ(z) = Hλ(z) - Hκ(z) produces symmetric/anti-symmetric responses that can be efficiently implemented
Solution Approach 2:
The patent transitions from processing the impulse response in the time domain to processing it in the polyphase domain with explicit symmetry exploitation. By finding complementary phases and forming symmetric/anti-symmetric combinations, the patent adds a dimensional transformation that enables simultaneous achievement of low-rate processing and multiplication reduction
Data Source
AI summary
The present invention is related to a circuit for converting the sample rate of a digital signal, comprisingan input for applying the digital signal,a conversion filter having either a symmetrical or anti-symmetrical impulse response and implemented as a plurality of subfilters in parallel, each subfilter having a symmetrical or anti-symmetrical response derived from components of a polyphase decomposition of said impulse response,combining means for deriving from said applied digital signal input signals of said plurality of subfilters or for combining output signals of said plurality of subfilters into a digital signal with converted sample rate,an output for outputting said digital signal with converted sample rate.