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I'm new to the topic of DFT and I need to understand the following question in detail because I'm a bit confused and I need to solve the requirements needed using any programming language

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so taking DFT discrete function into consideration. is the n in our function x(m) the sampling rate which is equal to 20? also is N the total number of samples which is 100?

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enter image description here also how to represent the signal x(t) to compute the DFT? and how to apply the comparison on the three cases. I know that in x(t) if we represented it as a relation between a frequency and amplitude, it would be a spike depending on the given value of t which should be either 0 or above and 0 otherwise. if there is any correction to what I understand, I would be really thankful.

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  • $\begingroup$ Look at (2) and (3) -- what do you think the prof meant with (3)? "how to represent the signal x(t) to compute the DFT" You are given $x(t)$, and you are given the sampling rate. What's missing, and how do you compute it? $\endgroup$
    – TimWescott
    Nov 18, 2021 at 21:21

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To answer the question, $n$ is not the sampling rate that is equal to 20, but $N$ is the total number of samples equal to 100. $n$ is a counting index that goes through each of those samples in turn, starting at index 0 and ending at 99. This puts the time domain in units of "samples" rather than units of "seconds".

So to represent $x[n]$ instead of $x(t)$, realize that the sampling rate will convert units of $t$ to units on $n$: since the sampling rate is 20 samples per second, consider then what would $t$ be for each sample? What is the duration of each sample in time? From this you can then determine $x[n]$ from $x(t)$ for each sample and then use the formula directly as written.

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  • $\begingroup$ thank you so much for your help. $\endgroup$
    – zamnas
    Nov 19, 2021 at 14:29

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