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Non-parametric impulse response estimation using input-output data

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impulseest() is a non-parametric impulse response estimation function with input-output data

As the variance increases linearly with the finite impulse response (FIR) model order, it is important for higher order FIR models to counteract this situation by regularizing the estimative. In impulseest(), this is done as proposed in T. Chen et al [2012] using the Empirical Bayes method (Carlin and Louis [1996]).

The six arguments in this function are:
- u [NumPy array]: input signal (size N x 1);
- y [NumPy array]: output signal (size N x 1);
- n [integer]: number of impulse response estimates (default is n = 100);
- RegularizationKernel [string]: regularization method - 'none', 'DC', 'DI', 'TC' (default is 'none');
- MinimizationMethod [string]: bound-constrained optimization method used to minimize the cost function - 'L-BFGS-B', 'Powell', 'TNC' (default is 'L-BFGS-B').

The impulseest function returns a NumPy array of size n x 1 containing all the n impulse response estimates. See https://www.sciencedirect.com/science/article/pii/S2352711021000832 for more details.

Importing

from impulseest import impulseest

Example

For a detailed example, please check the example folder. Basic usage:

ir_est = impulseest(u,y,n=100,RegularizationKernel='DC')

Contributor

Luan Vinícius Fiorio - [email protected]

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Non-parametric impulse response estimation using input-output data

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