I want to write a program in Java that uses fast Fourier transformation. The program reads data every 5 milliseconds seconds from sensors and is supposed to do something with the data every 200 milliseconds based on the data from the last five seconds.
Is there a good library in Java that provides a way to do Fourier transformation without recalculating all five seconds every time?
Hard real time problems are not the proper application of Java. There are too many variables such as Garbage collection and Threads not guaranteed to happen within a given interval to make this possible. If close enough is acceptable it will work. The performance of your software as far as timing will also depend on the OS and hardware you are using and what other programs are also running on that box.
There is a Real Time Java, that does have a special API for the issues I mention above. You do not indicate that you are using that. It is also a different animal in a lot of respects than plain Java.