!
hints and guiding questions 
!Depends on what is covered in the course. I would expect my students to be able to answer this question without too much thought, including even the complex phase of the frequency components.BvU said:
By looking at the function and the sampling rate i suppose we can conclude which going to be the main frequencies present in the DFT, but is it really possible to know the exact magnitude and phase of the DFT without actually doing the DFT ?DrClaude said:
With a ##y(t)## such as that given in the OP, yes. However, I cannot say more for now as it would help the OP too much.Delta2 said:
A discrete Fourier transform is a mathematical operation that converts a sequence of discrete data points into a representation of the data in the frequency domain. It is commonly used in signal processing and data analysis to analyze the frequencies present in a signal or dataset.
A DFT is a specific type of Fourier transform that is applied to discrete data points, while a Fourier transform can be applied to continuous functions. This means that a DFT is used to analyze data that is sampled at discrete intervals, while a Fourier transform can be used to analyze continuous signals.
A DFT has many applications in various fields, including signal processing, image processing, audio analysis, and data compression. It is also commonly used in the analysis of time series data in fields such as economics, physics, and engineering.
A DFT is typically calculated using an algorithm called the Fast Fourier Transform (FFT). This algorithm breaks down the DFT calculation into smaller, more manageable parts, making it more efficient to compute. There are also other methods for calculating a DFT, such as the Discrete Cosine Transform (DCT) and the Discrete Sine Transform (DST).
One limitation of a DFT is that it assumes the data is periodic, meaning that it repeats itself over a given interval. This can lead to inaccuracies when analyzing non-periodic data. Additionally, the DFT can only provide information about the frequencies present in a signal up to a certain frequency limit, known as the Nyquist frequency. Beyond this limit, aliasing can occur, which can distort the frequency information in the DFT.