The log-energy parameter, typically derived from a full-band spectrum, is a critical feature commonly used in automatic speech recognition (ASR) systems. However, log-energy is difficult to estimate reliably in the presence of background noise. In this paper, we theoretically show that background noise affects the trajectories of not only the 'conventional' log-energy, but also its delta parameters. This results in a poor estimation of the actual log-energy and its delta parameters, which no longer describe the speech signal. We thus propose a new method to estimate log-energy from a sub-band spectrum, followed by dynamic change enhancement and mean smoothing. We demonstrate the effectiveness of the proposed log-energy estimation and its post-processing steps through speech recognition experiments conducted on the in-car CENSREC-2 database. The proposed log-energy (together with its corresponding delta parameters) yields an average improvement of 32.8% compared with the baseline front-ends. Moreover, it is also shown that further improvement can be achieved by incorporating the new Mel-Frequency Cepstral Coefficients (MFCCs) obtained by non-linear spectral contrast stretching.