Speech analysis is the modelling and estimating of the different speech characteristics that would provide the importance on each set of criteria established on the real time applications. One such analytic section in enhancement process on speeches would improve the need of speech enhancement. This paper compares the performance analysis of our proposed Fast Hybrid Euclidean Direction Search (FHEDS) algorithm with other adaptive algorithms such as NHP and FEDS algorithm. These algorithms have been tested for their adaptive noise cancellation of speech signal corrupted by different noises such as Babble, Factory, Destroy Engine, Car, Fire Engine and Train Noises. Ensuring the design criteria with current design limits of the database and its analysis have been encapsulated with each phase of design with Noise model, improving the better performance aspects. The relative factors for comparisons have been tabulated with each set of the noise and clear speech data with proposed filter operation. The proposed model effectively reduces the noise for achieving better speech enhancement. The proposed model achieves high Signal-to-Noise Ratio (SNR) when compared to traditional models.