Dft filter banks
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DFT Filter Banks. Steven Liddell Prof. Justin Jonas. Channelization. A common task in radio astronomy is the channelization of a signal onto separate frequency channels. The output signal has a decreased bandwidth so the output sample rate can be decrease multirate systems.

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DFT Filter Banks

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DFT Filter Banks

Steven Liddell

Prof. Justin Jonas


Channelization

  • A common task in radio astronomy is the channelization of a signal onto separate frequency channels.

  • The output signal has a decreased bandwidth so the output sample rate can be decrease multirate systems.


Why Channelise a signal?

  • Allow computation to be performed on a narrower bandwidth and in parallel.

  • Implement the F in an FX correlator.

  • RFI mitigation.

  • Spectrum analysis.

  • Pulsar dedispersion


How to Channelize a Signal

  • Analogue filter banks.

    • Unstable; Would rather use digital signals.

  • Fast Fourier Transform.

    • Fast; Not a great frequency response.

  • Digital filter banks

    • More computation required; Get a good response.

    • Discrete Fourier Transform (DFT) filter banks.


  • FFT vs Filterbanks

    • FFT has a higher processing loss => decreases the instruments sensitivity.


    Computational Costs

    ≈N/2 log2(M) MACs

    M × N MACs


    DFT Filter Banks

    • DFT filter banks arise by modifying the FFT’s windowing function to provide channels with improved stop band attenuation and a narrower transition width.

    • The modified window is based on a prototype filter which lends its frequency response to each channel.

    • Two architectures of DFT looked at.


    DFT Filter Banks

    Weighted Overlap Add Filter Bank

    Polyphase Filter Bank

    ≈Mlog2(M)+N MACs


    The Polyphase Filter Bank

    • Replace a FFT’s window with a set of polyphase filters.

    • Create polyphase filters from a prototype filter:

    Prototype filter

    Polyphase filters (pρ(n))


    Prototype filter copied onto each channel.


    Aliasing

    Critically sampled

    (output data rate 1/16 input data rate)

    Over Sampled

    (output data rate >1/16 input data rate)


    Wola Filter Bank

    • The Weighted Overlap and Add filter bank.

    • Mathematically identical to polyphase filter.

    • Implementation different decouple number of channels from sample rate change factor.


    WOLA Filter Bank

    • Weighted

    Overlap

    Add:


    • Fixed point arithmetic leads to a errors in the system.

    • Quantization error can be modelled as noise injected at a multiplier.

    • Error occurs in both the FIR and FFT so need to balance the number of bits.


    Fixed point error in the filter coefficients change the channels’ frequency response.


    • Efficient through use of FFT but with good frequency response.

    • Easily implemented in parallel hardware.

    • Inherent sample rate change.

    • Replacing the stand alone FFT in signal paths requiring high accuracy channelization.


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