I find it helpful to think of the frequency-domain representation as a list of phasors. The Discrete Fourier Transform takes your time-domain signal and produces a list of phasors which, when summed together, will reproduce your signal. In very broad strokes, the two representations can be thought of as looking something like this,.
Continuity, Integration and Fourier Theory
We combine or sum phasors by stringing them together into a chain. Once the chain of phasors is constructed, we allow each phasor to begin rotating. We can reconstruct the time domain signal by tracing the vertical distance from the origin to the tip of the last phasor. In very broad strokes, the two representations can be thought of as looking something like this, We combine or sum phasors by stringing them together into a chain.
The absolute value of the Fourier transform represents the frequency value present in the original function and its complex argument represents the phase offset of the basic sinusoidal in that frequency.
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The Fourier transform is also called a generalization of the Fourier series. This term can also be applied to both the frequency domain representation and the mathematical function used.
The Fourier transform helps in extending the Fourier series to non-periodic functions, which allows viewing any function as a sum of simple sinusoids. Toggle navigation Menu.
Fourier Transform. Definition - What does Fourier Transform mean?
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Techopedia explains Fourier Transform The Fourier transform is a mathematical function that decomposes a waveform, which is a function of time, into the frequencies that make it up. The Fourier transform of a function f x is given by: Where F k can be obtained using inverse Fourier transform. Some of the properties of Fourier transform include: It is a linear transform — If g t and h t are two Fourier transforms given by G f and H f respectively, then the Fourier transform of the linear combination of g and t can be easily calculated. Time shift property — The Fourier transform of g t—a where a is a real number that shifts the original function has the same amount of shift in the magnitude of the spectrum.
An Interactive Guide To The Fourier Transform – BetterExplained
Modulation property — A function is modulated by another function when it is multiplied in time. Share this:. Related Terms.