If a basic sin sound wave is analysed with a Fourier transform, the result is just a spike at a certain frequency. My maths isn't the best so bare with me... if we take a real sound file and take Fourier transforms at regular intervals (I assume that's what's being done when calculating a Spectrum over a range of time of a sound file), I'll get a spectrum that doesn't any longer have spikes and instead has these more mountain peaks rather than spikes. My question is, since real sounds aren't stationary and taking into account the additivity of Fourier transforms (i.e. from my understanding, you can simply add Fourier transforms without um... data loss?), is the reason for these more mountain peaks rather than spikes simply due to the averaging process?