Frequency transformations for linear-phase variable-cutoff digital filters

Abstract

The first- and second-order forms of a transformation for implementing a variable-cutoff linear-phase FIR filter are investigated. In the first-order case, correct constraints have been placed on the variable parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_0</tex> ; it is pointed out that the cutoff frequency increases, while the cutoff slope decreases, monotonically with increasing <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_v; A_0 = 0</tex> corresponds to the prototype filter. The second-order transformation is shown to overcome these drawbacks without increasing the computational load or the number of variable parameters.