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What are the conditions for the existence of Fourier transform?
The conditions are: f must be absolutely integrable over a period. f must be of bounded variation in any given bounded interval. f must have a finite number of discontinuities in any given bounded interval, and the discontinuities cannot be infinite.
What is the sufficient condition for the existence of Dtft?
Sufficient Condition for Existence of the DTFT A sequence x[n] satisfying (7.7) is said to be absolutely summable, and when (7.7) holds, the infinite sum defining the DTFT X(ej ˆω) in (7.2) is said to converge to a finite result for all ˆω.
What does Fourier transform represent?
The Fourier Transform is an important image processing tool which is used to decompose an image into its sine and cosine components. The output of the transformation represents the image in the Fourier or frequency domain, while the input image is the spatial domain equivalent.
Are there sufficient conditions for the Fourier transform to exist?
Because the Fourier Transform is an integral over an infinite range, we must consider whether or not the integral converges. Sufficient conditions for the existence of the Fourier Transform are the Dirichlet conditions. That is, the Fourier Transform exists if:
Is the Fourier transform a square integrable signal?
This requirement can be stated as , meaning that belongs to the set of all signals having a finite norm ( ). It is similarly sufficient for to be square integrable, i.e. , or, . More generally, it suffices to show for [ 12, p. 47].
Is the Fourier transform in the frequency domain?
The Fourier Transform is another method for representing signals and systems in the frequency domain. is the continuous time Fourier transform of f ( t ). It is an extension of the Fourier Series. The Fourier transformation creates F ( ω ) in the FREQUENCY domain.