Design of digital IIR filter: A research survey

Abstract

This paper presents an overview on advancement made in designing of a digital infinite impulse response (IIR) filter. The design problem of an IIR filter was found to be challenging due to presence of poles in its transfer function. This makes the phase response of an IIR transfer function nonlinear and its magnitude response is also drifted due to quantization of coefficient values of denominator polynomials, which leads towards instability. Therefore, numerous efforts were made in order to acquire an optimal filter response using several optimization methods. Design problem of an IIR filter with various constraints was developed and solved using gradient based techniques, which resulted in optimal passband response with nearly linear phase or in some cases, absolute linearity was also achieved. However, the obtained solutions were sub-optimal in many cases due to transferring the multimodal design problem of an IIR filter into convex optimization. The solution was also affected due to the quantization of filter coefficients and in case of absolute linear phase response; a strong hick in magnitude response at beginning of transition edge frequency was obtained. To overcome the sub-optimality, researchers used evolutionary algorithms (EAs) for designing of an IIR filter. In time domain, system identification (SI) was adopted, whereas various error functions were developed in frequency domain for obtained magnitude responses close to desired response. This approach resulted in an optimal IIR filter response, however phase response linearity was not improved. Thus, EA approach was appropriated for lower order IIR filters. The design of various IIR filters like lowpass filter (LPF), highpass filter (HPF), bandpass filter (BPF) and bandstop filter (BSP) using an all-pass infinite impulse response (APF-IIR) was also reported. This approach is most appropriate, because the filter response is stable, nearly linear and magnitude response was also accurate. However, there is high error at the band edges of passband. Therefore, literature reveals that an APF based approach is most appropriate for various magnitude response filters.