## What Is Time-Domain Correlation Analysis?

Time-domain correlation analysis refers to non-parametric estimation of the impulse response of dynamic systems as a finite impulse response (FIR) model from the data. The estimated model is stored as transfer function model object (`idtf`). For information about transfer function models, see What are Transfer Function Models?.

Correlation analysis assumes a linear system and does not require a specific model structure.

Impulse response is the output signal that results when the input is an impulse and has the following definition for a discrete model:

The response to an input u(t) is equal to the convolution of the impulse response, as follows:

`$y\left(t\right)={\int }_{0}^{t}h\left(t-z\right)\cdot u\left(z\right)dz$`