Merged Delay Transformed IIR Down Sampler Filter: An efficient architecture and cost reduction technique for implementation

In this paper, an efficient Infinite Impulse Response Decimation Architecture based on conventional IIR filter using Merged Delay Transformation (MDT) is proposed. The technique explores that, by using the Merged Delay Transform, filtering as well as sampling rate compression (down sampling) is achieved in single stage instead of two separate stages as in conventional decimation recursive filter which in turn reduces the computational cost in terms of number of multipliers per output samples. The mathematical calculation and simulation results show that the computational cost reductions obtained by the proposed scheme are about 83.56%, 73.56% & 50.83% as compared to Polyphase FIR, Conventional IIR, Polyphase IIR, respectively which increases with higher value of M. The System Function of the transformed filter is evaluated in term of H(z<;sup>M<;/sup>). In this paper, M number of delay elements in recursive part of structure have been merged together from which the current output can be directly computed from M<;sup>th<;/sup> old output so that the computational efficiency is enhanced. Magnitude as well as Phase Response of various conventional filters (Butterworth, Chebyshev-I, Chebyshev-II and Elliptical IIR Filters) with or without MDT have been simulated and compared for different order at fixed Decimation Factor and for different Decimation Factor at fixed order using commercially available software. The simulation results show that there is no difference in magnitude as well as phase response of filters with or without the transformation so the transformed filter shows the good agreement with the original filter.