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DFT Filter Banks

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DFT Filter Banks

Steven Liddell

Prof. Justin Jonas

- 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.

- 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

- Analogue filter banks.
- Unstable; Would rather use digital signals.

- Fast; Not a great frequency response.

- More computation required; Get a good response.
- Discrete Fourier Transform (DFT) filter banks.

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

≈N/2 log2(M) MACs

M × N MACs

- 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.

Weighted Overlap Add Filter Bank

Polyphase Filter Bank

≈Mlog2(M)+N MACs

- 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.

Critically sampled

(output data rate 1/16 input data rate)

Over Sampled

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

- The Weighted Overlap and Add filter bank.
- Mathematically identical to polyphase filter.
- Implementation different decouple number of channels from sample rate change factor.

- 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.