Discrete Function - A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers. Explicit Definition - A definition of a function by a formula in terms of the variable.
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The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.
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Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.
The domain is the possible values that can be input into the function and produce a real number output.
Discrete means hidden or non visible. The discrete information should not be revealed.