Discrete amplitude spectrum

The shape of the amplitude spectrum is determined by the function sin( f ) f π τ π τ . the single rectangular pulse of width τ contains all frequencies between 0 and ∞. the relative amplitudes (ignoring the overall amplitude factor) of these frequencies is given by the function sin( f ) f π τ π τ .

The Fourier amplitude spectrum FS(ω) is defined as the square root of the sum of the squares of the real and imaginary parts of F(ω) . Thus: [2] Since a(t) has units of acceleration, FS(ω) has units of velocity. The Fourier amplitude spectrum is of interest to seismologists in characterizing ground motion.

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.