A Mathematical Miracle: Shazam

This paper investigates and explains the already established foundational mathematical system behind the application Shazam, focusing on the Fourier Transform and its applications in audio signal processing. It explains how the Fourier Transform helps in the decomposition of the complex audio input signals into their constituent frequencies, while the Fast Fourier Transform (FFT) is examined as an efficient computational algorithm. This paper also discusses the practical limitations of the Fourier Transform including, time truncation, spectral leakage, frequency resolution, and noise sensitivity.

To investigate the effect of noise sensitivity in input signals, an experimental study was conducted in which audio signals with varying signal-to-noise ratios (SNRs) were tested using Shazam. The results showed that decreasing the SNR increased identification time, and the accuracy had a sudden decrease when the noise power was set equal to the signal power and Shazam was not able to identify the song when the noise overpowered the input signal. Finally, the paper examines how Shazam overcomes these challenges through spectral peak extraction and audio fingerprinting, demonstrating the practical power of Fourier-based signal analysis.