This paper is focused on the theoretical analysis of the efficiency of Independent component analysis (ICA) based non-Gaussian signal representations corrupted by different types of noises. We first present a mathematical derivation demonstrating that ICA-based signal representations, in which the ICA transformation matrix was derived on clean non-Gaussian signals (denoted by ICAc) are efficient representations than DCT for signals when being both clean and corrupted by Gaussian noise, while it may not have better performance for the non-Gaussian noises corrupted signals. The analysis also demonstrates that to obtain efficient representations of non-Gaussian corrupted signals, the ICA transformation matrix should be obtained from noise corrupted signal (denoted by ICAn). The ICAn-based features can provide significant recognition accuracy improvements to non- Gaussian corrupted signals over both the ICAc-based features and MFCC features. Our findings are experimentally demonstrated by employing the ICA for speech feature extraction; specifically, the ICA is used to transform the logarithm filter-bank-energies (instead of the DCT which provides MFCC features). The evaluation is presented for a GMM-based speaker identification task on the TIMIT database for clean speech and speech corrupted by Gaussian noises and non- Gaussian noises.