This paper investigates the significance of combining cepstral features derived from the modified group delay function and from the short-time spectral magnitude like the MFCC. The conventional group delay function fails to capture the resonant structure and the dynamic range of the speech spectrum primarily due to pitch periodicity effects. The group delay function is modified to suppress these spikes and to restore the dynamic range of the speech spectrum. Cepstral features are derived from the modified group delay function, which are called the modified group delay feature (MODGDF). The complementarity and robustness of the MODGDF when compared to the MFCC are also analyzed using spectral reconstruction techniques. Combination of several spectral magnitude-based features and the MODGDF using feature fusion and likelihood combination is described. These features are then used for three speech processing tasks, namely, syllable, speaker, and language recognition. Results indicate that combining MODGDF with MFCC at the feature level gives significant improvements for speech recognition tasks in noise. Combining the MODGDF and the spectral magnitude-based features gives a significant increase in recognition performance of 11 % at best, while combining any two features derived from the spectral magnitude does not give any significant improvement.