Q:

Fourier series and Fourier transform. Amplitude spectrum vs. Frequency spectrum

I would like to know if there are any differences between amplitude spectrum and frequency spectrum. Is there any link between these two notions? 

A:

From here:
Any signal whose amplitude is a function of time has a corresponding frequency spectrum. When the signals are viewed in the form of a frequency spectrum, certain aspects of the signals or the underlying processes producing them are revealed. In some cases the frequency spectrum may include a distinct peak corresponding to a sine wave component. And additionally there may be peaks corresponding to harmonics of a fundamental peak, indicating a periodic signal which is not simply sinusoidal.
The power spectral density (PSD) of the signal describes the power present in the signal as a function of frequency, per unit frequency. Sometimes one encounters an amplitude spectral density (ASD), which is the square root of the PSD. This is useful when the shape of the spectrum is rather constant, since variations in the ASD will then be proportional to variations in the signal's amplitude itself. But it is mathematically preferred to use the PSD, since only in that case is the area under the curve meaningful in terms of actual power over all frequency or over a specified bandwidth.
In short, when we use the word spectrum or frequency spectrum, we are referring to the magnitude squared of its Fourier transform, which is a bit different from the PSD (See the third paragraph of this section). You may also refer to this question for more clarification of the terms.

