the samples x(n T). The sinc function h(t) = sinc t/T shifted to n T, i.e. h(t T), is equal to one at n T and zero at all other samples l T, l 6= n. The sum of the weighted shifted sincs will agree with all samples x(n T), n integer. A general reconstruction ﬁlter For the development of the theory, it is handy to consider the impulse-sampled ...

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The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces. The rectangular function can often be seen in signal processing as a representation of different signals. The sinc function, defined as sin t t, and the rectangular function form a Fourier transform pair.