Intelligibility listening tests are necessary during development and evaluation of speech processing algorithms, despite the fact that they are expensive and time-consuming.The proposed scheme uses a monaural intelligibility prediction algorithm, which has the potential of replacing some of the listening tests. The proposed algorithm shows similarities to the Short-Time Objective Intelligibility (STOI) algorithm but works for a larger range of input signals. In contrast to STOI, Extended STOI (ESTOI) does not assume mutual independence between frequency bands. ESTOI also incorporates spectral correlation by comparing complete 400-ms length spectrograms of the noisy/processed speech and the clean speech signals. As a consequence, ESTOI is also able to accurately predict the intelligibility of speech contaminated by temporally highly modulated noise sources in addition to noisy signals processed with time-frequency weighting. We show that ESTOI can be interpreted in terms of an orthogonal decomposition of short-time spectrograms into intelligibility subspaces, i.e., a ranking of spectrogram features according to their importance to intelligibility.