Keyword Analysis & Research: duality principle fourier
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Then we automatically know the Fourier Transform of the function G (t) : This is known as the duality property of the Fourier Transform. All of these properties can be proven via the definition of the Fourier Transform. On the next page, we'll look at the integration property of the Fourier Transform.What is the duality property and why is it useful?
In general, the Duality property is very useful because it can enable to solve Fourier Transforms that would be difficult to compute directly (such as taking the Fourier Transform of a sinc function).Is the Fourier transform of a sinc a rectangular pulse?
Then, according to the duality property we have the Fourier transform pair given that p(.) is even. So the Fourier transform of the sinc is a rectangular pulse in frequency, in the same way that the Fourier transform of a pulse in time is a sinc function in frequency.How do you find the Fourier transform of a signal?
Find the Fourier transform of x ( t) = A cos (Ω 0t) using duality. The Fourier transform of x ( t) cannot be computed using the integral definition since this signal is not absolutely integrable, or using the Laplace transform since x ( t) does not have a Laplace transform.