Mapping audio data to feature vectors for the classification, retrieval or identification tasks presents four principal challenges. The dimensionally of the input must be significantly reduced; the resulting features must be robust to likely distortions of the input; the features must be informative for the task at hand; and the feature extraction operation must be computationally efficient. In this paper, we propose Distortion Discriminant Analysis (DDA), which fulfills all four of these requirements. DDA constructs a linear, convolutional neural network out of layers, each of which performs an oriented PCA dimensional reduction. We demonstrate the effectiveness of DDA on two audio fingerprinting tasks: searching for 500 audio clips in 36 h of audio test data; and playing over 10 days of audio against a database with approximately 240 000 fingerprints. We show that the system is robust to kinds of noise that are not present in the training procedure. In the large test, the system gives a false positive rate of 1.5 × 10-8 per audio clip, per fingerprint, at a false negative rate of 0.2% per clip.