No that's not right. The FFT is not infinite dimensional. It's the same dimension as whatever length FFT you take. The FFT is just a set of algorithms for computing the DFT. In general they work by recursively decomposing an N-length DFT into shorter length DFT's.
The DTFT on the other hand is "infinite" dimensional in that it takes an infinite time series as input and outputs a continuous spectrum with period of 2pi.
Comments
No that's not right. The FFT is not infinite dimensional. It's the same dimension as whatever length FFT you take. The FFT is just a set of algorithms for computing the DFT. In general they work by recursively decomposing an N-length DFT into shorter length DFT's.
The DTFT on the other hand is "infinite" dimensional in that it takes an infinite time series as input and outputs a continuous spectrum with period of 2pi.
Sorry, This is embarrassing, I must have not drank my coffee... Of course you are right.