finite impulse response (filter) (FIR)
FIR filters(Finite Impulse Response) are feedback-free, phase-linear digital filters with finite impulse response whose filtered values y(n) are calculated from a specific, just past history of the input signal x. In the FIR filter, the calculation of the y value refers to the finite past. A characteristic of this is that any amplitude changeat the input must have decayed after passing through all delay stages at the output.
The function of a FIR filter can be compared, as an example, with the formation of a moving average. Here, the sum of "n" consecutive values is formed and this is divided by "n". After that, the group of n-values is continuously shifted one bar at a time and the mean value is formed again each time. The result is a sequence of filtered values that have passed through a kind of low-pass filter whose cutoff frequency decreases with the number of passes. The frequency response resulting from this example cannot be used in practice. Therefore one uses other mathematical relations with the FIR method. So first each value is divided by "n" before all quotients are summed.
A FIR filter has the simple structure of a delay line with taps, where the number of taps is multiplied by a coefficient and the sum is the output. The two variables are the number of taps and the value of the coefficients. Such digital filters are usually determined by their" order", which is the number of delay elements. Thus, a 2nd order filter has two delay elements and three taps.
The disadvantage of FIR filters is that increasing complexity of the filter curve, for example due to steep filter slopes, increases the computational cost. FIR filters have a linear phase response with frequency-independent magnitude frequency response and constant group delay. Due to the constant phase response, no pulse distortions occur.