Fourier Transform

The Fourier Transform of x(t), a continuos signal, enables the analysis in frequency of this signal.

The signal x(t) represents a value in each time instant, the signal X(jw), Fourier Transform of x(t), represents a value for each frequency, for example:

x(t) = cos(2t), X(jw) = 0.5 to w = 2 and w = -2, in this case x(t) has only frequency in 2 and -2 radians/s.

The Fourier Transform is defined by:

We observe the operation and see that X(jw) is obtain from a superposition of exp(-jwt) over x(t), for each w.

The Fourier Transform is a linear and biunivocal transform, so the Inverse Fourier Transform is:


Using the Fourier Transform is possible do analysis of any signal, as thermical, physical, electrical, electromagnetic spectrum, etc.....