Abstract: A new method for extracting fingerprints from waveforms (e.g. musical signals) is disclosed, alosng with exemplary apparatus for doing same, all being particularly useful for recogizing waveforms. The new method is based on the principle of calculating features based on in-band frequency changes over time, in addition to the in-band amplitude changes over time considered by previous method according to the present invention s. Database lookup using these fingerprints is robust to a variety of changes that impair the signal, include lossy coding/decoding; dynamic compression; speed change; mixture with interfering signals, including speech and white noise at 0 dB SNR; and convolution with complex filters, including the effect of cell-phone transmission in an error-prone channel. The new method's performance has been evaluated on a large set of controlled test cases. Optimizations for improving search efficiency on large databases with approximate matching are also discussed.