DFT Filter Banks

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DFT Filter Banks

• Steven Liddell
• Prof. Justin Jonas

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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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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

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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.

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FFT vs Filterbanks

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

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Computational Costs
N/2 log2(M) MACs
M N MACs
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DFT Filter Banks

• DFT filter banks arise by modifying the FFTs
  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.

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DFT Filter Banks
Weighted Overlap Add Filter Bank
Polyphase Filter Bank
Mlog2(M)N MACs
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The Polyphase Filter Bank

• Replace a FFTs window with a set of polyphase
  filters.
• Create polyphase filters from a prototype filter

Prototype filter
Polyphase filters (p?(n))
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Prototype filter copied onto each channel.
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Aliasing
Critically sampled (output data rate 1/16 input
data rate)
Over Sampled (output data rate gt1/16 input data
rate)
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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.

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WOLA Filter Bank

• Weighted

Overlap
Add
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• 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.

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