Inverse Fourier transformation

The inverse Fourier transform is a mathematical formula that converts a signal in the frequency domain ω to one in the time (or spatial) domain t.

A time domain signal f(t) is obtained by demodulating a frequency domain signal F(ω) using a special sinusoidal wave e across all time (from negative infinity to positive infinity) via:

  • f(t)  = [1/(2 π)] ·  ∫ F(ω) · e dω

j represents a square root of -1(an imaginary number); e is a sinusoidal wave with an imaginary component as per Euler's formula:

  • e = cos(ωt) + j · sin(ωt)

Conversely, time domain signals can be converted to frequency domain signals via the Fourier transform.