High Quality Content by WIKIPEDIA articles! Mathematical notation aside, the motivation behind integral transforms is easy to understand. There are many classes of problems that are difficult to solve—or at least quite unwieldy algebraically—in their original representations. An integral transform "maps" an equation from its original "domain" (e.g., functions where time is the independent variable are said to be in the time domain) into another domain. Manipulating and solving the equation in the target domain is, ideally, much easier than manipulation and solution in the original domain. The solution is then mapped back to the original domain with the inverse of the integral transform. Integral transforms work because they are based upon the concept of spectral factorization over orthonormal bases. What this means is that many important arbitrarily complicated functions can be represented as sums of much simpler functions.

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