Speech coding facilitates speech compression without perceptual loss that results in the elimination or deterioration of both speech and speaker specific features used for a wide range of applications like automatic speaker and speech recognition, biometric authentication, prosody evaluations etc. The present work investigates the effect of speech coding in the quality of features which include Mel Frequency Cepstral Coefficients, Gammatone Frequency Cepstral Coefficients, Power-Normalized Cepstral Coefficients, Perceptual Linear Prediction Cepstral Coefficients, Rasta-Perceptual Linear Prediction Cepstral Coefficients, Residue Cepstrum Coefficients and Linear Predictive Coding-derived cepstral coefficients extracted from codec compressed speech. The codecs selected for this study are G.711, G.729, G.722.2, Enhanced Voice Services, Mixed Excitation Linear Prediction and also three codecs based on compressive sensing frame work. The analysis also includes the variation in the quality of extracted features with various bit-rates supported by Enhanced Voice Services, G.722.2 and compressive sensing codecs. The quality analysis of extracted epochs, fundamental frequency and formants estimated from codec compressed speech was also performed here. In the case of various features extracted from the output of selected codecs, the variation introduced by Mixed Excitation Linear Prediction codec is the least due to its unique method for the representation of excitation. In the case of compressive sensing based codecs, there is a drastic improvement in the quality of extracted features with the augmentation of bit rate due to the waveform type coding used in compressive sensing based codecs. For the most popular Code Excited Linear Prediction codec based on Analysis-by-Synthesis coding paradigm, the impact of Linear Predictive Coding order in feature extraction is investigated. There is an improvement in the quality of extracted features with the order of linear prediction and the optimum performance is obtained for Linear Predictive Coding order between 20 and 30, and this varies with gender and statistical characteristics of speech. Even though the basic motive of a codec is to compress single voice source, the performance of codecs in multi speaker environment is also studied, which is the most common environment in majority of the speech processing applications. Here, the multi speaker environment with two speakers is considered and there is an augmentation in the quality of individual speeches with increase in diversity of mixtures that are passed through codecs. The perceptual quality of individual speeches extracted from the codec compressed speech is almost same for both Mixed Excitation Linear Prediction and Enhanced Voice Services codecs but regarding the preservation of features, the Mixed Excitation Linear Prediction codec has shown a superior performance over Enhanced Voice Services codec.