In the field of digital signal processing, the function of a filter is to remove unwanted parts of the signal such as random noise that is also undesirable. To remove noise from the speech signal transmission or to extract useful parts of the signal such as the components lying within a certain frequency range, filters are necessary. Filters are broadly used in signal processing and communication systems in applications such as channel equalization, noise reduction, radar, audio processing, speech signal processing, video processing, biomedical signal processing that is noisy ECG, EEG, EMG signal filtering, electrical circuit analysis and analysis of economic and financial data. In this paper, three types of infinite impulse response filter i.e. Butterworth, Chebyshev type I and Elliptical filter have been discussed theoretically and experimentally. Butterworth, Chebyshev type I and elliptic low pass, high pass, band pass and band stop filter have been designed in this paper using MATLAB Software. The impulse responses, magnitude responses, phase responses of Butterworth, Chebyshev type I and Elliptical filter for filtering the speech signal have been observed in this paper. Analyzing the Speech signal, its sampling rate and spectrum response have also been found.