For existence of DTFT of a signal should be absolutely summable is a*
Question
For existence of DTFT of a signal should be absolutely summable is a*
Solution
The Discrete Time Fourier Transform (DTFT) of a signal exists if the signal is absolutely summable. This means that the sum of the absolute values of the signal samples is finite.
Here are the steps to check if a signal is absolutely summable:
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Take the absolute value of each sample in the signal. This means if you have a signal x[n] = {3, -2, 1, -4}, you would transform it to |x[n]| = {3, 2, 1, 4}.
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Sum all the absolute values together. Using the example above, you would calculate 3 + 2 + 1 + 4 = 10.
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If the sum is finite, then the signal is absolutely summable and the DTFT of the signal exists. In this case, 10 is a finite number, so the DTFT of the signal exists.
Remember, this is a necessary condition for the existence of the DTFT. It doesn't guarantee that the DTFT will exist, but if the signal is not absolutely summable, then the DTFT definitely does not exist.
Similar Questions
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