Design and FPGA Implementation of Reconfigurable Linear-Phase Digital Filter withWide Cutoff Frequency Range and NarrowTransition Bandwidth
Abstract : Reconfigurable filters based on the spectral parameter approximation (SPA) technique and its combination with other techniques provide a continuous control over the cutoff frequency (fc). However, when very wide fc range and narrow transition bandwidth is desired, these filters either fail to satisfy some of the specifications or have extremely high complexity. In this brief, we propose an interpolated SPA filter (ISPA filter) which overcomes all the limitations of all the existing SPA technique based filters, and achieves very wide fc range (equal to approximately the entire Nyquist band) and narrow transition bandwidth along with small passband ripple and high stopband attenuation. Comparison with the state-ofthe-art reconfigurable filters is provided via a design example, which shows that the ISPA filter achieves more than 50% savings in the number of multipliers compared to the filter based on the combination of SPA and modified coefficient decimation techniques. The FPGA implementation results show that the ISPA filter has much lesser group delay and much higher operating speed, but incurs moderate penalty in terms of area compared to the filter based on the combination of frequency transformation and interpolation techniques.
? 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 may have finer control over the bandwidth and allowable bandwidth can be any value which is an integer multiple of the bandwidth of the resource block (which 180 KHz in existing standard).
? When compared with existing FDSs, the CVFD element provides wide fractional delay range at the minimum multiplication complexity possible, and is capable of changing the fractional delay range on-the-fly.
? To overcome these disadvantages of variable coefficient filters, reconfigurable filters are developed in which fc is varied using only a couple of variable parameters by modifying the impulse response of the fixed-coefficient prototype filter.
? To address these problems, overdesign of the prototype filter is used which results in the requirement of higher order prototype filters that increase the implementation complexity of the VCF filters.
? Linear programming based filter design technique proposed in can also be used to address this problem.
? In, prototype filter design is considered as an optimization problem with the required set of coefficient decimation factors and desired stopband attenuations considered beforehand as constraints.
• A lot of novel design approaches have been proposed for the design of area efficient, low complexity VCF FIR filters.
• The interpolation approach was first proposed to obtain a low complexity narrow transition bandwidth filter from a relatively wider transition bandwidth filter and was later adapted for the design of VCF filters.
• VCF filter based on the combination of CDM and first-order APT based technique was proposed in and a lower complexity alternative to it was proposed in by combining ICDM and the first-order APT.
• An interpolated SPA (ISPA) based filter was proposed in to extend the cutoff frequency range of the SPA based filters to entire Nyquist band, by integrating SPA and interpolation techniques.
? It is an efficient way of designing low complexity narrow tbw variable filter.
? However, as the desired fc range becomes wider and/or the desired transition bandwidth (tbw) becomes narrower, the complexity of SPA based filters increases rapidly along with the values of the sub-filter coefficients, making the fixed-point implementation difficult.
? In the coefficient decimation (CDM) technique, impulse response of the filter is modified either by replacing (by zero) or by discarding the filter coefficients other than every Dth coefficient.
? The SPA filter provides continuous control over fc in the given tuning range, has approximately same group delay as the variable coefficient filter, and has constant tbw for all the responses.
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