# DFT explanation for a given signal providing samples per second and total samples

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

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?

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.

• 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? Nov 18, 2021 at 21:21

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.