The Robust Transform based on the Weighted Median operator algorithm calculates the transform of a signal when it has been exposed to impulsive noise. Since this algorithm demands very long execution time, it is not useful for real time signal processing systems. In this context, this work presents several strategies to improve its performance, such as the reduction of redundant calculations, optimization in the memory access, and a multithreads version of the algorithm. Besides, the original estimation method is modified to decrease even more the average execution time, keeping the quality level of the numeric results. The experimental results show a 30% performance improvement by reducing redundant calculations and optimizing the memory access, without making modifications to the estimation method and without using multi-threaded processing; 93% performance improvement by introducing modifications to the estimation method; and 97% performance improvement by incorporating the multi-threaded processing.