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# filter

filters a data sequence using a digital filter

### Syntax

[y,zf] = filter(B, A, x [,zi])

### Arguments

- B
real vector : the coefficients of the filter numerator in decreasing power order, or a polynomial.

- A
real vector : the coefficients of the filter denominator in decreasing power order, or a polynomial.

- x
real row vector : the input signal

- zi
real row vector of length

`max(length(a),length(b))-1`

: the initial condition relative to a "direct form II transposed" state space representation. The default value is a vector filled with zeros.- y
real row vector : the filtered signal.

- zf
real row vector : the final state. It can be used to filter a next batch of the input signal.

### Description

This function filters a data sequence using a digital filter using a "direct form II transposed" implementation.

The filter canonical form is :

The algorithm uses the highest degree between `degree(a)`

and `degree(b)`

as value for `n`

.

If the polynomial form is used for `B`

(resp. for `A`

) then a polynomial or a scalar must be used for `A`

(resp. `B`

).

### References

Oppenheim, A. V. and R.W. Schafer. Discrete-Time Signal Processing, Englewood Cliffs, NJ: Prentice-Hall, 1989, pp. 311-312.

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