Tornado Infrasound Filtering and Prediction Vocabulary

Vocabulary and engineering concepts for infrasound signal processing, filtering (FIR, IIR, DWT, Kalman), and predictive modelling (LMS, AR).

Hann Window

A window function used for the FFT and spectrogram to reduce spectral leakage by tapering record endpoints toward zero.

Hamming Window

A window function used in FIR design to truncate the ideal impulse response with lower first-sidelobe leakage than a rectangular window.

Nyquist Frequency

The highest frequency that can be represented in a sampled signal, equal to half the sampling frequency ($500\,Hz$ in this project).

Spectral Leakage

The spreading of energy from one frequency into neighbouring FFT bins because the observed record is finite and its endpoints are discontinuous.

RMS (Root Mean Square)

A measure of average energy over a block used for event detection that is less sensitive to isolated spikes than peak amplitude.

Linear Phase

A filter property where phase is proportional to frequency, resulting in a constant group delay and preservation of waveform shape and relative timing.

Group Delay

The delay experienced by the envelope or features of a signal; for a symmetric FIR filter of length $N$, it is calculated as $\frac{N-1}{2}$ samples.

Type-I FIR Filter

A symmetric FIR filter with an odd length and even order that can realise general low-pass, high-pass, band-pass, and band-stop responses.

Butterworth Filter

An IIR filter design based on an analogue prototype that achieves a monotonic, maximally flat passband with no ripple.

Prewarping

The process of adjusting analogue design frequencies so the bilinear transform maps them to the intended digital edge frequencies.

Digital Poles

Roots of the transfer-function denominator or AR characteristic polynomial; for stability, they must lie inside the unit circle.

DWT Approximation

The low-frequency branch of the Discrete Wavelet Transform resulting from repeated low-pass filtering and downsampling.

DWT Detail

the frequency band removed at each level of the Discrete Wavelet Transform by the high-pass branch.

Shift Variance

A limitation of the critically sampled DWT where a small time shift in the input can significantly change the coefficient distribution and reconstructed waveform.

Kalman Filter

A recursive state estimator that estimates hidden states—such as pressure, pressure rate, and pressure acceleration—using a physical model and measurement uncertainty.

Q (Process-noise covariance)

A Kalman filter parameter representing uncertainty in the state model; larger values make the filter follow measurements more quickly.

R (Measurement-noise covariance)

A Kalman filter parameter representing microphone measurement uncertainty; larger values result in a smoother estimate that relies more on the model.

Kalman Gain

The weighting factor calculated from predicted covariance and measurement uncertainty that balances the state prediction and the new measurement.

Innovation

In Kalman filtering, the difference between the actual measurement and the measurement predicted from the state model.

Wiener LMS Predictor

A predictor that uses the Least Mean Square (LMS) iterative method to approach the minimum-mean-square-error Wiener solution.

LMS Excess MSE

The remaining fluctuation around the optimum solution in an LMS filter caused by a finite step size.

AR(10)

A tenth-order Autoregressive model where each new sample is represented as a weighted combination of the previous 10 samples plus an error term.

Recursive Multi-step Prediction

A forecasting method where the model predicts one sample, appends it to the history, and repeats the process until the desired horizon is reached.

Condition Number

A measure of the sensitivity of a fitted solution to numerical changes; large numbers indicate nearly dependent columns in a regression matrix.

Normalised RMSE (NRMSE)

Root Mean Square Error divided by the target standard deviation, used to compare error across signals with different amplitudes.

TDOA (Time Difference of Arrival)

A method used to estimate the bearing of a source by calculating the relative timing delay between signals received at different microphones.