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This book provides an extensive study of available literature on various filtering techniques used for speech enhancement. In this book, a new method is introduced for improvement of speech distorted by acoustic noise which is based on spectral subtraction technique. Here, noise estimation is done through a new proposed algorithm based on adaptive cascaded median filter. The developed model results in elimination of musical noise which is introduced by conventional cascaded median filter. This algorithm is tested on various noisy speech samples taken from NOIZEUS database sampled at 8 kHz and then processed using a hamming window of length 250 ms with an overlap size of 128 ms. Moreover, this algorithm is also capable of tackling the non-stationary nature of noise. Various listening tests were performed in order to judge the quality and intelligibility. For the performance analysis of the given model, the parameters selected are root mean square error (MSE) and perception evaluation of speech quality (PESQ) scores. The developed algorithm shows an improvement of 20-55 % in PESQ scores over CCM filter.