We propose a new scheme to reduce phase sensitivity in independent component analysis (ICA)-based feature extraction using an analytical description of the ICA-adapted basis functions. Furthermore, since the basis functions are not shift invariant, we extend the method to include a spectral-domain ICA stage that removes redundant time shift information. The performance of the new scheme is evaluated for TIMIT phoneme recognition and compared with the standard mel frequency cepstral coefficient (MFCC) feature.