Fourier analysis has many scientific applications -- in physics , partial differential equations , number theory , combinatorics , signal processing , imaging , probability theory , statistics , option pricing , cryptography , numerical analysis , acoustics , oceanography , sonar , optics , diffraction , geometry , protein structure analysis , and other areas .
Fourier analysis is widely used in fields such as physics , partial differential equations , number theory , combinatorics , signal processing , imaging , probability theory , statistics , option pricing , cryptography , numerical analysis , acoustics , oceanography , sonar , optics , diffraction , geometry and protein structure analysis .