This paper provides an in-depth examination of crucial signal processing methods essential for analyzing and interpreting various signals, particularly in the realm of speech. The reviewed techniques include the Fourier transform, Mel-Frequency Cepstral Coefficients (MFCCs), Hidden Markov Models (HMMs), Deep Neural Networks (DNNs), and waveform coding. The applications of these methods in speech signal processing are elucidated, highlighting their specific advantages and inherent limitations. The paper also explores challenges associated with signal processing, such as the impact of noise, equipment quality, and computational demands. Emphasizing the need to carefully choose the appropriate signal processing technique for a given task, the review underscores the importance of striking a balance between the strengths and weaknesses of each method to achieve effective signal enhancement and analysis.