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 ejωt across all time (from negative infinity to positive infinity) via:
- f(t) = [1/(2 π)] · ∫ F(ω) · ejωt dω
j represents a square root of -1(an imaginary number); ejωt is a sinusoidal wave with an imaginary component as per Euler's formula:
- ejωt = cos(ωt) + j · sin(ωt)
Conversely, time domain signals can be converted to frequency domain signals via the Fourier transform.
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