In this paper, a new transformation polynomial for s-to-z plane is presented. This third-order transformation is derived by optimising the coefficients of the logarithmic series followed by utilising the multirate technique to extend its bandwidth. In terms of magnitude and phase response, the proposed transform correlates well with the ideal and shows mean absolute magnitude error and mean absolute phase error as 40 dB and 132:04 dB, respectively. The proposed transform is compared with the existing operators to demonstrate its performance. In addition, an example is also conferred, which establishes the viability of the transform in terms of the overall frequency response, when applied for analog-to-digital transformation.