Designing of adaptive bandpass filter with adjustable notch for frequency demodulation

The state variables of an internal model controller in a feedback loop can provide direct estimate of the instantaneous frequency of a signal. An adaptive algorithm to identify and track the instantaneous frequency was developed in our previous works (L.J. Brown et. al., 2002, June 2003). This approach has as design parameters a fictitious plant and feedback controller. This paper presents a strategy for choosing the transfer functions of the fictitious plant and controller to incorporate a desired filter in the scheme. By choosing and designing the suitable forms and coefficients of transfer functions for the controller and plant in the system, a bandpass filter with an adjustable notch can be achieved. The location of the notch frequency is adjusted in the range of bandwidth by our adaptive algorithm. It is shown that a bandpass filter characteristics enhances the ability of the algorithm to reject noise. However, simulations show that this benefit comes at the expense of slower transient characteristics of the feedback loop which has negative consequence for identification of the instantaneous frequency.