- After I generate the code, how can I use it as a part of my MATLAB code? Is the generated code intended to be used in an execution environement other than MATLAB?
It depends if you compile as stand alone then it is not intended to be used in MATLAB. The only option is compile in MEX.
- It seems like the fft function in MATLAB is already using FFTW. Then, what is the purpose of generateing FFTW library calls from MATLAB function? Does it really speedup the computation?
No, it is only interesting for people who compile in Stand alone or source code to be used elsewhere and reproduce similar behavioir as MATLAB FFT, based on FFTW.
I personally tried to interface FFTW library on C-code and used under MATLAB, I'm not able to make it as fast as MATLAB FFT. I believe Matlab FFT is compiled with better compiler/option than mine and it is quite hard to beat it.
However if you have good grahics card you might try to do FFT with GPU.