Transform theory

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of <a href="/facts/Basis_(linear_algebra)/89IPoN6c">basis</a> for a <a href="/facts/Vector_space/M1pxMLx2">vector space</a> a problem may be simplified—or diagonalized as in <a href="/facts/Spectral_theory/8sAEEIMM">spectral theory</a>.
Main examples of transforms that are both well known and widely applicable include <a href="/facts/Integral_transform/AB2yjHJJ">integral transforms</a> such as the <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a>, the <a href="/facts/Fractional_Fourier_transform/kwH2qV0M">fractional Fourier Transform</a>, the <a href="/facts/Laplace_transform/0Ge4MIc9">Laplace transform</a>, and <a href="/facts/Linear_canonical_transformation/TTUqqAfV">linear canonical transformations</a>. These transformations are used in <a href="/facts/Signal_processing/Npaja6zb">signal processing</a>, <a href="/facts/Optics/p0vq4S1T">optics</a>, and <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>.

Transform theory open-in-new

Transform theory