Many signal processing applications require digital filters with variable frequency characteristics, especially the filters with variable bandwidth. Due to their linear phase and inherent stability, variable bandwidth finite impulse response (FIR) filters are the popular choice in majority of the applications. Once a variable cutoff frequency (VCF) FIR lowpass filter is designed, variable bandwidth bandpass / highpass / bandstop filters and reconfigurable filter banks can be realized from the same. In this paper, we present a comprehensive review of the existing variable cutoff frequency FIR filter design techniques, including the developments in the recent two decades. We provide the basic concepts, design and architectural details for each of these techniques and the major developments / incremental works thereof. Qualitative as well as quantitative comparisons are provided to assist the reader in choosing the most suitable VCF filter design technique for a particular application.
Keywords
FIR filters, reconfigurable filters, variable digital filters
IntroductionCompared to analog filters, digital filters have advantage of higher accuracy, exact linear-phase (if desired), time-invariant performance (analog filter performance changes due to component drift), relatively smaller silicon area etc. These advantages, coupled with the advent of VLSI technology, have resulted in ubiquitous presence of digital filters in almost all the signal processing applications with a few exceptions (such as wideband filtering in radio frequency range, which is not feasible due to the bottleneck at the speed of analog-to-digital converters).Digital filters with variable frequency response characteristics are required for numerous critical applications in the fields of digital communications, audio signal processing, biomedical signal processing etc. [1,2]. In digital communications domain alone, digital filters with variable frequency response characteristics can be used for spectrum analysis, spectrum shaping, channelization, and receiver synchronization. For e.g., a digital filter having tuneable passband and transition bandwidths is used for channel extraction in a multi-standard wireless communication receiver, as it needs to be interoperable with multiple communication standards having distinct bandwidth specifications. Alternatively, a digital modem uses a digital filter to implement variable fractional delays. In general, a digital filter whose frequency response can be changed on-the-fly is called a variable digital filter. Even though such a definition means that all the parameters related to the frequency response should be variable, in practice, majority of the applications demand only a lowpass filter with variable cutoff frequency (fc), satisfying the desired minimum specifications of transition bandwidth (tbw), passband ripple (δp) and stopband ripple (δs). Therefore, the VCF (variable cutoff frequency) filter design task can be simplified further, by specifying the maximum limit on tbw, δp, and δs, and thus, only one...