Let’s assume that we have performed a 20-point DFT on a sequence of real-valued
ID: 1839437 • Letter: L
Question
Let’s assume that we have performed a 20-point DFT on a sequence of real-valued time-domain samples, and we want to send our X(m) DFT results to a colleague using e-mail. What is the absolute minimum number of (complex) frequency-domain sample values we will need to type in our e-mail so that our colleague has complete information regarding our DFT results? Let’s assume that we have performed a 20-point DFT on a sequence of real-valued time-domain samples, and we want to send our X(m) DFT results to a colleague using e-mail. What is the absolute minimum number of (complex) frequency-domain sample values we will need to type in our e-mail so that our colleague has complete information regarding our DFT results?Explanation / Answer
ANSWER:
We need to send 20 values.
Irrespective of whether it is a time domain or frequency domain sample, every signal needs some minimum number of pieces of information to be re-constructed. If it needs 20 time domain samples, even in frequency domain, 20 equally-spaced samples are sufficient.
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