Acoustics

Alignments

A popular way to determine the ideal parameters has been through the use of alignments. The concept of alignments is based upon filter theory. Filter development is a method of selecting the poles (and possibly zeros) of a transfer function to meet a particular design criterion. The criteria are the desired properties of a magnitude-squared transfer function, which in this case is | H(s) | ². From any of the design criteria, the poles (and possibly zeros) of | H(s) | ² are found, which can then be used to calculate the numerator and denominator. This is the ?optimal? transfer function, which has coefficients that are matched to the parameters of | H(s) | ² to compute the appropriate values that will yield a design that meets the criteria.

There are many different types of filter designs, each which have trade-offs associated with them. However, this design is limited because of the structure of | H(s) | ². In particular, it has the structure of a fourth-order high-pass filter with all zeros at s = 0. Therefore, only those filter design methods which produce a low-pass filter with only poles will be acceptable methods to use. From the traditional set of algorithms, only Butterworth and Chebyshev low-pass filters have only poles. In addition, another type of filter called a quasi-Butterworth filter can also be used, which has similar properties to a Butterworth filter. These three algorithms are fairly simple, thus they are the most popular. When these low-pass filters are converted to high-pass filters, the transformation produces s⁸ in the numerator.

More details regarding filter theory and these relationships can be found in numerous resources, including [5].