Deconvolutie

The system's impulse response can be utilized to determine the output response through input signal and impulse response convolution.

Acquiring this impulse response, given an input signal and output, is called deconvolution or inverse filtering. It is the process of obtaining one of the constituent signals in the convolution sum.

Given an input signal and an output response, deconvolution can be performed using polynomial division or recursive algorithm methods to yield the impulse response.

In the polynomial division approach, sequences are seen as coefficients of descending-order polynomials. Long division is then executed to obtain the impulse response.

In the recursive algorithm method, the output response is initially defined as the convolution sum, which can be formulated as a recursive algorithm. The equation is simplified by setting the variable n to zero, allowing the impulse response for positive values of n to be obtained.

The number of evaluations needed for the impulse response is determined by substituting signal lengths into the given relation. The final impulse response value is calculated for the obtained number.