To match dimension,
where,
Friday, November 13, 2015
Relation Between Fourier Series and Fourier Transform
To see the relation between them, use dimensional analysis. Suppose the signal is dimensionless, then the dimension of its Fourier transform is [TIME], but the coefficient of Fourier series is by definition dimensionless, so it has to be multiplied by a quantity with dimension of [TIME] to get involved with Fourier Transform.
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