all the sinusoids in that band and add them up – remember that it is a complex
addition. Since there are infinite components in Δ
ω
, the sum of infinitesimal
amplitudes need not be an infinitesimal. Now, divide the sum by Δ
ω
. We get
a quantity that has the dimensions of volt per rad/sec (assuming an aperiodic
voltage waveform). Repeat the process with a smaller Δ
ω
around the same
ω
. We will observe that the ratio – which is the density of spectral amplitudes
at and around
ω
– approaches a limit as we reduce Δ
ω
to zero. Fourier
transform value at
ω
is this limiting density of spectral amplitudes multiplied
by 2
π
. Hence, Fourier transform is a spectral amplitude ...
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