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

DFT Filter Banks

Steven Liddell

Prof. Justin Jonas


Channelization

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

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

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 vs Filterbanks

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


    Computational costs

    Computational Costs

    ≈N/2 log2(M) MACs

    M × N MACs


    Dft filter banks1

    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 banks2

    DFT Filter Banks

    Weighted Overlap Add Filter Bank

    Polyphase Filter Bank

    ≈Mlog2(M)+N MACs


    The polyphase filter bank

    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))


    Dft filter banks

    Prototype filter copied onto each channel.


    Aliasing

    Aliasing

    Critically sampled

    (output data rate 1/16 input data rate)

    Over Sampled

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


    Wola filter bank

    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 bank1

    WOLA Filter Bank

    • Weighted

    Overlap

    Add:


    Dft filter banks

    • 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.


    Dft filter banks

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


    Dft filter banks

    • 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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