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What is a band-limited function?

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What is a band-limited function?

(a) A function of limited duration whose highest frequency is finite

(b) A function of limited duration whose highest frequency is infinite

(c) All of the mentioned

(d) None of the mentioned

This question was posed to me during an internship interview.

Query is from Spatial and Gray-Level Resolution and Aliasing topic in portion Image Enhancement of Digital Image Processing

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The correct answer is (a) A function of limited duration whose highest frequency is finite

The explanation is: Functions whose area under the curve is finite can be represented in terms of sines and cosines of various frequencies. The highest frequency is determined by the sine/cosine component is the highest “frequency content” of the function. If this highest frequency is finite and that the function is of unlimited duration, then, these functions are called band-limited functions.

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