A known limitation of ft/dft is that it requires an infinite series of sinusoids
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Fourier series is the decomposition of a periodic signal into infinite sum ... Now, we all know that both periodic and aperiodic signals exist in the world. ... we take the limit of the frequency as tending to zero(since period -> infinity). ... This is often stated as: a periodic function has a discrete Fourier transform.
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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. Because no real number satisfies this equation, i is called an imaginary number. For the complex number a + bi, a is called the real part, and b is called the imaginary part. Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers, and are fundamental in many aspects of the scientific description of the natural world.
Complex numbers allow solutions
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