Frequency transformations for linear-phase variable-cutoff digital filters

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
A_0
; it is pointed out that the cutoff frequency increases, while the cutoff slope decreases, monotonically with increasing
A_v; A_0 = 0
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.