Q: "I would also request a review of the material we have covered so far. I am getting confused about what and how each of the transforms are different than each other and why we need them."
A: About the transforms, please see page 1 of the transforms notes posted on the Resources page. This picture was provided to help all of us keep these transforms straight in our mind. So far, we have talked about the CTFT and CTFS (briefly) and the DTFT and DTFS in more detail. We are now starting to talk about the DFT. Later in the semester we will discuss the FFT and the z-transform. Which transform you use depends on situation. If you are analyzing a continuous time signal or system, use the CTFT. If the signal is periodic, then the CTFT does not really exist, but can be obtained by first expanding the signal in a Fourier series (CTFS) and then transforming using the CTFT. On the other hand, if you are analyzing a discrete-time signal or system, use the DTFT. If the signal is periodic (or a power signal), then the DTFT does not exist at some frequencies. Delta functions are used in expressing the DTFT of these signals. Fourier series expansions can be used for periodic signals. We have defined the DFT of a finite length signal as the DTFS of the periodic signal obtained by periodically replicating the given signal.
No comments:
Post a Comment