ANALYZE OF NONRECURSIVE FILTERS OR FIR

1. Recurrence equation

FIR filters have a transfer function polynomial which contains a big number of coefficients.They are
 unconditionally stable. Knowing that filter FIR is systems for which a output value is obtained by a balanced sum a set finished by input values representing the samples of the signal to be leaked out, one has: With M the order of the filter. Remark :  a FIR filter of order M has M+1 coefficients.

2. Structure of realization

2.1. Direct structure Application requires for every output value M multiplications and M additions. It is necessary also M+1 memories for coefficients and M+1 data memories . The functioning of this structure is put rhythm in the time by the sample period . One realizes so this operation : 2.2 Transposed structure Here, cells with delay memorize partial sums. One realizes in output filter the calculation of .

Remark : It is noticed that there is no loop of reaction , one does not so use the values of the previous output to calculate current output. It is for it that such a filter is called filter nonrecursive.

 Impulse answer is the answer to the causal sequence . One has so : or :  etc ...

The coefficients of level-headedness are so the values of the impulse answer of the filter. This answer nullifies at the end of M+1 values ( more coefficients). Impulse answer being finished,one speaks about filter FIR.

 It is the signal answer to the causal signal . One has so : or :  etc...

The final value of the indexed answer is equal to the sum the coefficients of the filter FIR and is reached at the end of M+1 output.

 The transfer function in z spells : To have answer in frequency, one replaces z by , one has so : This answer is periodic of frequency .