Design of variable linear phase FIR filters based on second order frequency transformations and coefficient decimation

This paper presents the design of a variable linear phase finite impulse response filter based on second order frequency transformations and coefficient decimation. The design of variable digital filters (VDFs) using first and second order frequency transformations have been proposed in literature. The VDF using second order transformation has better cut-off slope characteristics compared to the VDF using first order transformation. However, the former has the drawback of limited range (approximately 25% of the half of the sampling frequency) over which the cut-off frequency, f_c, can be varied. It also fails to provide variable lowpass, highpass, bandpass or bandstop responses from a fixed-coefficient lowpass filter using the same architecture. The architecture proposed here overcomes the above mentioned disadvantages using coefficient decimation technique. The design example shows that the range over which f_c can be varied is 2.65 times wider in the proposed VDF than the VDF in [7] and for a given frequency range, the proposed VDF offers a total gate count saving of 33% and 41% over the VDF in [11] and [7] respectively. Also, the proposed architecture provides variable lowpass, highpass, bandpass or bandstop responses from a fixed coefficient lowpass filter.