Stability analysis and finite word length effect on Merged Delay Transformed IIR Down Sampler Filters

In this paper, stability of Merged Delay Transformed Infinite Impulse Response Decimation Filters or IIR Down Sampler Filters has been determined and compared with stability of original IIR Decimation Filters without Merged Delay Transform. The Merged Delay Transform provides an efficient architecture to implement the IIR Down Sampler Filter and It is also the computational cost reduction technique of implementation. The stability of transformed transfer functions for all types of IIR Filters (Butterwort, Chebyshev-I, Chebyshev-II and Elliptical IIR Filters) are investigated on the basis of the location of poles and zeros. It is observed that the proposed MDT introduced M-1 number of additional poles and equal number of zeros within the unit circle. The additional zeros have the concurrent position with the additional poles. The simulation results show that the stability of transformed IIR decimation filters (all cases) will not be disturbed as the decimation factor M increases. The simulation results also show that the transformed Elliptic filter is more stable whereas the transformed Chebyshev-II is marginally stable filter. In this paper, the peak error between the output from the proposed transformed filters and from the original filter is also investigated for various values of decimation factor M and the simulation result shows that this peak error is in the range of 10^-10 to 10^-17 which increases with increase in filter order. The finite word length effect on transformed filters as well as original filters is investigated for filter order n=2 and M=8 by quantizing the data values. By changing the bits for quantization, effect of shift in poles and zeros position of the system function due to Merged Delay Transformation is also studied.