# Applications¶

## Pulse and Shape Detection, Baseline Separation¶

Rectangular Pulse Detection with Baseline [ex111.0] – Detection of rectangular pulses in noisy signle-channel signal superimposed by a baseline wander signal.

ECG Shape Detection [ex113.0] – Detection of pulses of known shapes and separation of the pulses from a superimposed additive baseline wander.

Rectangular Pulse Detection with Baseline [ex111.0] – Detection of neuronal spikes in a multi-channel signal.

## Model Switch and Edge Detection¶

Edge Detection [ex110.0] – Detection of abrupt slope changes in a single-channel signal.

## Linear Filters with ALSSMs¶

Symmetric linear filter with ALSSMs using a covariance steady-state matrix (speed enhancement) [ex121.0] – Applying an ALSSM as a symmetric (i.e., forward-backward) linear filter on a multi-channel signal.

Multi-Channel Symmetric Signal Filter [ex120.0] – Applying an ALSSM as a symmetric (i.e., forward-backward) linear filter on a single-channel signal. Uses steady-state of covariance matrix to substantially increase computation speed.

## Polynomial Calculus & Cost Terms¶

Poly-to-poly fit [ex210.0] – Fitting of a polynomial of lower order to a polynomial of higher order over a given time interval.

Squared error between two polynomials [ex211.0] – Closed form computation of the squared error between two time-continuous polynomials.