Define Spectrum of Real Signals?

In the real world, we rarely come throughout a pure sine wave. Typical signals have a wide spectrum as displayed in the above diagram. Information above or below a fixed frequency or amplitude is usually considered surplus to requirements. For instance, hi-fi manufacturers assume that 20kHz is the highest frequency that the ear can detect.

Assuming that fm is the maximum frequency of interest in a signal, after that we would like to sample at the Nyquist Rate, that is at f_s = 2f_m (the sampling frequency = twice the maximum frequency). If we go ahead and sample at 2f_m, we get a spectrum as shown in the top diagram. The bands overlap and we generate aliasing in the output signal. To prevent this, we must first make use of a low-pass filter on the input signal to eliminate any frequency components above f_m.