I am applying to graduate school in US. I am wondering how I can write statement of purpose If I am interested in both signal processing and communication system. Should I talk about why I am interested in both and talk about researches and projects I have done in both areas and my future research in both fields since I like both equally?. However I was thinking this is too much and is going to pass the word limit for statement of purpose. I am looking for some advice about this. Any advice will be greatly appreciated.
I assume when you say "communication" you mean an area of engineering closely allied to signal processing, rather than communication in the context of the arts or social sciences.
In this case, you may as well just talk about some specific problems you are interested in, without worrying too much about how to categorize them. If you can talk in detail and with confidence about your past projects and potential future plans, then you can write a good statement of purpose. It is more important to spend words on demonstrating your understanding of the actual research problems (What do you want to do? Why is it important? Why is it hard? Why is it original? etc.) than on classifying topics within the overall field. The former is what readers really want to know about.