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The usual techniques of conditioning on RV s or Jacobian transformations are no longer required if Mellin transform properties are applied; and the transform of the productpdf can be readily converted to moments of the compound channel pdf.
The transform of is defined by (1.1).
and are the transform of and respectively.
Thus the transform of can be expressed as (34).
The transform of the signal is defined by (5).
The transform of (3) gives the multiplication of the signal's ambiguity function with the transform of the kernel.
Similar(18)
The Fourier transform of the convolution equals the product of the spectra (Fourier transforms) of the convolved functions.
Envelopes were calculated using the absolute value of the Hilbert transform of the impulse response.
Next, the Fourier transform of the measured data is calculated.
Since is the Fourier transform of the function (4.23).
be the Fourier transform of the function f ( x ).
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