EECS20N: Signals and Systems

Linearity of Fourier Transforms

Consider discrete time signals x(n), x1(n), x2(n), related by

x(n) = a x1(n) + bx2(n).

Then it is easy to see from the definition of the DTFT that

X(ω ) = aX1(ω ) + bX2(ω )

where X = DTFT (x), X1 = DTFT (x1), and X2 = DTFT (x2).

The same linearity property applies to the CTFT.