Mel Frequency Cepstral Coefficients (MFCCs) are the most popularly used speech features in most speech and speaker recognition applications. In this paper, we study the effect of resampling a speech signal on these speech features. We first derive a relationship between the MFCC param- eters of the resampled speech and the MFCC parameters of the original speech. We propose six methods of calculating the MFCC parameters of downsampled speech by transforming the Mel filter bank used to com- pute MFCC of the original speech. We then experimentally compute the MFCC parameters of the down sampled speech using the proposed meth- ods and compute the Pearson coefficient between the MFCC parameters of the downsampled speech and that of the original speech to identify the most effective choice of Mel-filter band that enables the computed MFCC of the resampled speech to be as close as possible to the original speech sample MFCC.