## FIfBiquad

#### Routine

void FIfBiquad (const float x[], float y[], int Nout, const float h[5])

#### Purpose

Filter a signal using a biquadratic IIR filter

#### Description

This procedure forms the output of an IIR filter. The output is a biquadratic section with the z-transform,

             h[0]*z^2 + h[1]*z + h[2]
      H(z) = ------------------------ .
               z^2 + h[3]*z + h[4]

The output is formed using the following relationship,

      y[i] = h[0]*x[i] + h[1]*x[i-1] + h[2]*x[i-2]
                                     - h[3]*y[i-1] - h[4]*y[i-2] .

The filtering procedure needs the present and past two input samples and the past two output samples to form a new output sample. These are supplied as extensions to the input and output arrays.

The input array x and the output array y can share storage. Consider an array A with Nout+4 elements. Let the first two elements (A[0] and A[1]) represent past output values. The next two elements (A[2] and A[3]) are past input values. The next Nout elements starting with A[4] are new input values. In this case, this routine can be invoked as

      FIbiquad (&A[2], &A[0], Nout, h)

On output Nout new output values are placed starting at A[2], overlaying the input values. The last two input values (A[Nout+2] and A[Nout+3]) remain intact. These along with the last two output values (A[Nout] and A[Nout+1]) are suitable for priming the array for processing the next group of samples. This can be achieved by moving the top 4 elements of the array to the bottom of the array and appending Nout new input values.

#### Parameters

-> const float x[]
  Input array with Nout+2 elements. The first two elements, x[0] and x[1], represent past input samples. The next Nout samples are the current input samples.
<-> float y[]
  Output array with Nout+2 elements. The first two elements, y[0] and y[1], represent past outputs and must be supplied as input. The remaining Nout elements are defined by this routine.
-> int Nout
  Number of output samples
-> const float h[5]
  Array of 5 filter coefficients defining the biquadratic filter section

#### Author / revision

P. Kabal / Revision 1.12 2003/05/09

#### See Also

FIfFiltIIR

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