To compute the response of a filter for a given signal, the convolution of the signal and the filter is taken. This mathematical operation is meant to alter the original signal with a specific goal. This could be e.g. filtering out certain frequencies from the signal.
| \( x \) | This symbol represents a function that represents a signal. |
| \( h \) | This is the symbol for a Finite Impulse Response (FIR), the unit Impulse Response (\( \htmlClass{sdt-0000000113}{h} \)) of a FIR filter. Because the result of this happens to be equal to the coefficients of the FIR filter, it is commonly also used to represent the FIR filter. |
| \( y \) | This symbol represents a response of a filter, meaning the output of a filter when a signal is put through it. |
| \( \ast \) | This symbol represents convolution, a mathematical operation on two functions resulting in a third function. The convolution is obtained by taking the integral of the product of the two functions after reflecting one of the two function about the y-axis and shifting it. |
| \( n \) | This symbol represents any given whole number, \( n \in \htmlClass{sdt-0000000014}{\mathbb{W}}\). |