convolution – Antenna pattern in frequency domain and Hamming window

I have an antenna pattern (azimuth cut) and I want to apply a Hamming window to it. In SAR processing the target is shaped by the azimuth antenna pattern, and on top of it it should be possible to apply a window. So the antenna pattern can be regarded as in the (Doppler) frequency domain. How can apply a window? I have tried to convert the pattern back to the time domain, multiply by the window and back again to frequency without success. Maybe I’m missing the understanding of time and frequency windows, sampling rate, etc..

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