ABSTRACT
Jean Baptiste Joseph Fourier was born in 1768 in France. Euler was 61 years old and Sir Isaac Newton had died only 42 years prior. To put that into a more musical context, Mozart was 12 years old when Fourier arrived, and wrote his seventh and eighth symphonies that same year. The hop size is the number of samples between the frames, and the overlap is the amount of the frame that is reprocessed on the next step. If the hop size equals the frame length then there is no overlap. The smaller the hop, the more overlap and vice versa. The criteria for a perfect reconstruction of the signal are called the Constant Over-Lap Add constraints. The constraints always come down to the window type that is used and the amount of overlap between frames. The phase vocoder can also be used to stretch or shrink time.
