Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 36

Convolution and multiplication of signals are often used in radar signal processing. As listed in Eqs. 1.12 and 1.13, convolution is the inverse operation of multiplication as the FT is concerned, and vice versa. This useful feature of the FT is widely used in signal and image processing applications. It is obvious that the multiplication operation is significantly faster and easier to deal with when compared to the convolution operation, especially for long signals. Instead of directly convolving two signals in the time domain, therefore, it is much easier and faster to take the IFT of the multiplication of the spectrums of those signals as shown below:

(1.18)

In a dual manner, convolution between the frequency‐domain signals can be calculated in a much faster and easier way by taking the FT of the product of their time‐domain versions as formulated below:

(1.19)