The Fourier transform is a mathematical formula that converts a signal in time (or spatial) domain t to one in the frequency domain ω.
A frequency domain signal F(ω) is obtained by modulating the time domain signal f(t) to a special sinusoidal wave e-jωt across all time (from negative infinity to positive infinity).
- F(ω) = ∫ f(t) · e-jωt dt
j represents a square root of -1(an imaginary number); e-jωt is a sinusoidal wave with an imaginary component as per Euler's formula:
- e-jωt = cos(ωt) - j · sin(ωt)
Conversely, frequency domain signals can be converted to time domain signals via the inverse Fourier transform.
Note: There are many websites that provide good explanations and visual examples of the Fourier transform that are worth exploring 3,4.
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