"Your phone captures sound as a waveform using a very thin membrane. This waveform is not useful for song identification, so a process called the Fast Fourier Transform is used to convert it into a three-dimensional representation of sound called a spectrogram."
"The raw waveform itself isn't very useful for identification. A song played louder produces a completely different waveform even though it's the same song. Two different songs can produce very similar waveforms, and the same song played in different environments can produce different waveforms."
"The trick is to transform the waveform into something more useful for a computer. Your phone runs a mathematical operation called a Fast Fourier Transform"
A phone records sound as a digitized waveform representing air pressure over time. The raw waveform varies with loudness and environment, so it is not reliable for identifying songs. A Fast Fourier Transform converts the waveform into a spectrogram, a time-frequency representation of sound. Shazam then creates an audio fingerprint from distinctive patterns in the spectrogram. The fingerprint is compared against a large database of precomputed fingerprints for many songs. Even with background noise and different playback conditions, the distinctive time-frequency features allow the system to find the best match quickly.
Read at Perthirtysix
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