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Signal processing & communications

Digital filters and spectra, radio physical and MAC layers, channel coding and satellite positioning.

Filters & spectra

Filtering, resampling and analysing sampled signals.

IIR and FIR filters

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Two ways to shape a sampled signal's spectrum: FIR (finite taps, always stable, exact linear phase) or IIR (feedback, a few coefficients, cheap but phase-distorting).

FIR O(N) multiply-adds per sample for N taps; IIR O(order) per sample, typically 5 per biquad

biquad filters

Planned.

Short-time Fourier transform and spectrogram

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Slide a window over a signal and FFT each frame to get a time-frequency picture; the front end of audio ML, vibration and radar analysis.

O(N log N) per frame of N samples; (L/hop) frames, so about (L/hop)*N*log2(N) work for L samples

fft convolution

Planned.

sample rate conversion

Planned.

wavelet transform

Planned.

peak detection

Planned.

Phase-locked loop (digital)

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Feedback loop that locks a local oscillator to the phase and frequency of an input tone; the core of carrier recovery, clock recovery and GNSS tracking.

O(1) per sample: one phase detector, two multiply-adds for the PI filter, one NCO update (sin/cos of the phase)

vibration spectral analysis

Planned.

dynamic time warping

Planned.

ppg heart rate estimation

Planned.

zero suppression

Planned.

Radio physical layer

Modulation, synchronization and detection in digital radios.

ofdm modulation

Planned.

ofdm time frequency synchronization

Planned.

qam soft demapping

Planned.

channel estimation

Planned.

mimo detection

Planned.

beamforming

Planned.

adaptive equalization

Planned.

symbol timing recovery

Planned.

digital down conversion

Planned.

chirp spread spectrum

Planned.

Radio access & MAC

Sharing the medium among many radios.

aloha random access

Planned.

rfid backscatter protocol

Planned.

tdma scheduling

Planned.

proportional fair scheduling

Planned.

airtime fairness

Planned.

dynamic bandwidth allocation

Planned.

ranging and delay equalization

Planned.

handover management

Planned.

client steering

Planned.

mesh routing

Planned.

robust header compression

Planned.

ble gatt

Planned.

Channel coding

Error-correcting codes and retransmission schemes.

Reed-Solomon codes

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Byte-oriented MDS code: n-k parity symbols correct (n-k)/2 unknown symbol errors or n-k known erasures; the workhorse for bursts, QR codes, discs and storage.

encode O(n(n-k)) field mults; decode O(n(n-k)) syndromes + O((n-k)^2) Berlekamp-Massey + O(n(n-k)) Chien search

Convolutional codes and the Viterbi decoder

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Streaming error-correcting code: each output bit is a parity of the last K input bits; the Viterbi decoder finds the most likely path through a 2^(K-1)-state trellis.

encode O(1) per bit; decode O(2^(K-1)) add-compare-select per bit (64 for K=7); traceback memory O(2^(K-1) x depth) bits

turbo codes

Planned.

ldpc codes

Planned.

polar codes

Planned.

hamming codes

Planned.

hybrid arq

Planned.

forward error correction

Planned.

line coding scrambling

Planned.

Satellite & radio positioning

Finding where a receiver or transmitter is.

gnss signal acquisition

Planned.

gnss tracking loops

Planned.

pseudorange least squares positioning

Planned.

rtk ambiguity resolution

Planned.

multilateration tdoa

Planned.