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# filter2

filter2 -- Performs filtering using a transposed form-II digital filter lattice with no time-varying control.

## Description

General purpose custom filter with time-varying pole control. The filter coefficients implement the following difference equation:

(1)*y(n) = b0*x[n] + b1*x[n-1] +...+ bM*x[n-M] - a1*y[n-1] -...- aN*y[n-N]

the system function for which is represented by:

B(Z) b0 + b1*Z-1 + ... + bM*Z-M
H(Z) = ---- = --------------------------
A(Z) 1 + a1*Z-1 + ... + aN*Z-N

## Syntax

ar filter2 asig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN

kr filter2 ksig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN

## Initialization

At initialization the number of zeros and poles of the filter are specified along with the corresponding zero and pole coefficients. The coefficients must be obtained by an external filter-design application such as Matlab and specified directly or loaded into a table via GEN01.

## Performance

The filter2 opcodes perform filtering using a transposed form-II digital filter lattice with no time-varying control.

Since filter2 implements generalized recursive filters, it can be used to specify a large range of general DSP algorithms. For example, a digital waveguide can be implemented for musical instrument modeling using a pair of delayr and delayw opcodes in conjunction with the filter2 opcode.

## Examples

A first-order linear-phase lowpass linear-phase FIR filter operating on a k-rate signal:

    k1 filter2 ksig, 2, 0, 0.5, 0.5   ;; k-rate FIR filter

## See Also

zfilter2

## Credits

Author: Michael A. Casey
M.I.T.
Cambridge, Mass.
1997

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