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Digital Filters

This document outlines the essential requirements for digital filters in signal processing, focusing on avoiding non-linearity during the analog-to-digital conversion. Emphasizing the importance of sufficient bit representation for signal clarity, it highlights the effectiveness of FIR filters and their configuration for optimal performance. The practicality of half-band filters and polyphase filter banks is discussed, particularly in their application for the Allen Telescope Array. Technical insights include the isolation of interference and maintaining dynamic range, emphasizing collaboration on future designs.

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Digital Filters

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  1. Digital Filters Mike Davis

  2. Requirements • Avoid non-linearity up to and through the analog to digital (A/D) converter • Use enough bits to adequately represent the signal plus noise plus interference (6 dB/bit) • Use enough bits in the weighting factors not to lose dynamic range • Count only effective A/D bits (typically 6.5 to 7 for a good 8-bit A/D converter)

  3. Filter Design • Finite Impulse Response (FIR) filters provide a tapped delay line, with complex weights at each tap • The impulse response corresponds to the tap weights. In principle, any impulse response can be created with an adequate number of taps

  4. Practical Filters • Half-band filters • Commercially available • Can be cascaded for multiple octave bandwidth selection • Used in Arecibo correlator very successfully • Polyphase Filter Banks • Arrangement to get reproducibly identical filter shapes in EACH frequency bin

  5. F-X Correlator Design for the Allen Telescope Array • Uses Polyphase Filter Bank for each of 350 antennas, with Field Programmable Gate Arrays • Outputs are cross-correlated for each pair of antennas, for each frequency • Isolation of interference by steep-sided frequency bin shape • Stay tuned – Matt Dexter is designing details of the PFB at Berkeley

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