The Fourier transform usually transforms a mathematical function of time, f(t), into a new function usually denoted by F() whose arguments is frequency with units of cycles/sec (hertz) or radians per second. This new function is known as the Fourier transform. The Fourier transform is a mathematical transformation used within many applications in physics and engineering. The term "Fourier transform" refers to both the transform operation and to the complex-valued function it produces.
The rectangular function can often be seen in signal processing as a representation of different signals. The sinc function, defined as , and the rectangular function form a Fourier transform pair.
The Fourier transform of F(t) = is:
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Where:
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= hertz
= a constant
j = imaginary number
Rect = rectangular function
sinc = sinc function
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The bandwidth or the range of frequency of the function is ≈