An introduction to spectrum analysis

Spectrum analysis is fundamentally important for spectral modelling because samples alone do not inform the spectral constituents of a sampled sound. In order to model the spectrum of sounds, musicians need adequate means to dissect, interpret and represent them. A number of methods have been created to analyse the spectrum of sounds. There are two categories of spectrum analysis harmonic and formant. 

Short-time Fourier transform (SIFT) stands for an adaptation, suitable for computer programming, of the original Fourier analysis mathematics for calculating harmonic spectra. 

It is important to bear in mind that there are at least four other terms that are closely related to STFT, which are prone to cause confusion Fourier transform (FT), discrete-time Fourier transform (DTFT), discrete Fourier transform (DFT) and fast Fourier transform (FFT). An in-depth discussion of the differences between these terms is beyond the scope of this book. On the whole, they differ in the way that they consider time and frequency, as follows  

1 FT is the original Fourier analysis mathematics whereby time and frequency are continuous 

2 DTFT is a variation of FT in which time is discrete, but frequency is continuous 

---