This paper proposes a new, simple and efficient technique in discrete-time domain which does the processing of auto correlation of the input discrete-time wide sense stationary (WSS) process through exponential, rectangular, triangular and trapezoidal shaped discrete time windows in linear time. The proposed algorithm also performs the Low Pass Filtering (LPF) of the input auto correlation in linear time since the frequency responses of the above mentioned discrete-time windows very much resemble with the frequency response of low pass filters. First, we develop the proposed algorithm for a discrete-time exponential shaped window having =M‘ samples and show that it takes O(L) arithmetic operations (i.e., both +s and *s) in processing the input auto correlation through it, where =L‘ is the size of input auto correlation sequence. We then, make use of this result in processing the input auto correlation through a rectangular shaped (moving average) window by incorporating a slight modification in it. Subsequently, we process the input auto correlation through triangular and trapezoidal shaped discrete-time windows using the modified result of the proposed algorithm. We thus show that our proposed algorithm only requires O(L) additions to perform the low pass filtering of the input auto-correlation through the last three windows mentioned above. We also show that the proposed algorithm just takes 2 x (L - 1) additions to perform the LPF of the input auto correlation through a rectangular shaped window and it remains independent with respect to the change in the size of the window, i.e., M. Finally, we also show that our proposed algorithm outperforms all the existing techniques in both time and frequency domains with regards to exact number of arithmetic operations and its worst case time complexity grows linearly with the length of the input auto correlation sequence for the case when L >> M.