
But, v
e
(t) is an even function of time, and hence, its Fourier transform must have
only a real part. Similarly, v
o
(t) is an odd function of time, and hence, its Fourier transform
must have only an imaginary part. Therefore, we conclude that
14.5.5 v(0) and V(j0)
The analysis integral evaluated at t ⫽ 0 reveals an interesting relation between the Fourier
transform value at
ω ⫽
0 and the total area content of the time-function. They are equal.
Hence, Fourier transform of a real time-function can not have an imaginary part at
ω
⫽ 0.
Similarly, the synthesis integral evaluated at t ⫽ 0 reveals that the value of time-
function at t ⫽ 0 is proportional to the ...