Polynomial Filter (Forensics Only)

[Craig Maier]

Polynomial Filter

(Forensics Version Only – Advanced Filters)

This allows mathematicians, scientists, and engineers to create their own transfer function using a polynomial expression. For those not so inclined, there is a plentiful assortment of presets to choose from. Also, there are two methods of data entry possible, either numerical or graphical.

This system realizes a transfer function in terms of the input to output signal ratios. It is useful for canceling the non-linearity’s that may have been introduced during a recording process. Essentially, this feature can be useful in some circumstances for reducing harmonic distortion that was created by the recording process non-linearity. The method of data entry for the Transfer Function is in the form of the coefficients associated with a 5^th order polynomial for which the actual transfer function graph is plotted automatically. You can enter the coefficients numerically for each term or you can use one of the numerous presets that are provided to get you started with a particular function. It is useful to have some mathematical background in order to effectively use this filter using coefficient data entry. However, trial and error is the best method for finding a setting that will reduce the distortion of a particular recording since the recording non-linearity is not generally known ahead of time. Furthermore, sometimes adding non-linearity’s can be useful to enhance the intelligibility of extremely muffled conversations. Limited instantaneous dynamic expansion and compression can also be realized by using this feature, for which there are several presets provided for convenience. Interesting distortion creation and frequency multiplication is also possible with this algorithm.


The Polynomial Filter

1. The Transfer Function is given in the general form by the following polynomial expression:

Y = A5X^5 + A4X^4 + A3X^3 + A2X^2 + A1X + A0

You have 6 fields in which you can enter the coefficients of the polynomial equation, including:
A5 =_____ A4 = _____ A3 =_____ A2 =_____
A1 =_____ A0 =_____

Note: Values of A can be positive or negative.

• Input Gain:

Range: 0.001 to 1.999 (1.000 represents unity gain.)
This controls the level of the signal being applied to the input of the polynomial expression.

• DC Offset :

Range: -1.00 to 0 to +1.00 (0 represents no DC offset value.)
This control effects the DC offset applied to the input signal to the equation.

• Output Gain:

Range: 0.001 to 5.000 (1.000 represents unity gain.)
This control effects the output level of this system after the polynomial equation has been applied to the signal.

• Mix:

Range: 0.000 to 1.000
This control effects the degree to which the processed signal is added to the input signal for presentation to the systems output. Zero (0) represents no polynomial effect and 1.000 represents complete polynomial effect on the output.

• Filter Type:

You can choose between “Polynomial” or “Spline” modes via the radio buttons. In “Polynomial” mode, you create your transfer function by entering your data as coefficients ranging from A0 to A5 in the appropriate numerical fields. If you choose “Spline”, you can create the transfer function you desire graphically by manipulating (with your mouse) the 4 square shaped inflection points presented on the graphical display.