Window Functions in Fourier Transform: Understanding the Role of Observation Time in Pitch Analysis
In the world of music analysis and signal processing, the Fourier transform is a powerful tool for understanding the frequency content of a sound. One of the key components of the Fourier transform is the window function, which controls how long the computer "looks" at the signal in order to determine the frequencies present. In a perfect world, a longer observation time would provide better accuracy in identifying the frequencies present in a sound. However, in the real world, musical notes from instruments are not infinitely long and their sustain is not always perfectly flat and clear. As a result, the pitch of a note can fluctuate, which can lead to a noisy spectrum when analyzing the sound. To address this problem, different window functions have been developed to control the observation time and minimize the impact of pitch fluctuations on the analysis. In music analysis, this principle can be applied to the frequency and time domain of a sound. A commonly used window f...