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Is there a way to compute efficiently the Fourier transform of the max of two functions (f,g), knowing their Fourier transform?
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As T→∞, 1/T=ω0/2π. Since ω0 is very small (as T gets large, replace it by the quantity dω). As before, we write ω=nω0 and X(ω)=Tcn. A little work (and replacing the sum by an integral) yields the synthesis equation of the Fourier Transform.
The Fourier transform is a type of mathematical function that splits a waveform, which is a time function, into the type of frequencies that it is made of. The result generated by the Fourier transform is always a complex-valued frequency function.
Fourier Transform: Fourier transform is the input tool that is used to decompose an image into its sine and cosine components. Properties of Fourier Transform: Linearity: Addition of two functions corresponding to the addition of the two frequency spectrum is called the linearity.
The Fourier transform is commonly used to convert a signal in the time spectrum to a frequency spectrum. Examples of time spectra are sound waves, electricity, mechanical vibrations etc. The figure below shows 0,25 seconds of Kendrick's tune. As can clearly be seen it looks like a wave with different frequencies.
I doubt it. The Fourier transform of max(f, g) can be computed efficiently if and only if the Fourier transform of |f| can be computed efficiently. (Because max(f,g) = (f+g+|f-g|)/2.)
But there seems to be no relationship between F{f} and F{|f|}...
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Assuming you mean the max at each point, and since max is a non-linear operation, there is not going to be any way to do this. You would need to do the max operation in the time domain and then perform the Fourier transform.
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