In this paper we describe a new framework of feature compensation for robust speech recognition, which is suitable especially for small devices. We introduce Delta-cepstrum Normalization (DCN) that normalizes not only cepstral coefficients, but also their time-derivatives. Cepstral Mean Normalization (CMN) and Mean and Variance Normalization (MVN) are fast and efficient algorithms of environmental adaptation, and have been used widely. In those algorithms, normalization was applied to cepstral coefficients to reduce the irrelevant information from them, but such a normalization was not applied to time-derivative parameters because the reduction of the irrelevant information was not enough. However, Histogram Equalization (HEQ) provides better compensation and can be applied even to the delta and delta-delta cepstra. We investigate various implementation of DCN, and show that we can achieve the best performance when the normalization of the cepstra and the delta cepstra can be mutually interdependent. We evaluate the performance of DCN using speech data recorded by a PDA. DCN provides significant improvements compared to HEQ. It is shown that DCN gives 15% relative word error rate reduction from HEQ. We also examine the possibility of combining Vector Taylor Series (VTS) and DCN. Even though some combinations do not improve the performance of VTS, it is shown that the best combination gives the better performance than VTS alone. Finally, the advantage of DCN in terms of the computation speed is also discussed.