# Are there windows that create asymmetric sidelobes

I am working on a project which uses radar imaging. The radar imaging takes place at a relatively small distance from the radar (0.25m to 3m). The data is collected using an FMCW radar. The FFT of the collected data is taken to calculate the target range. I want to reduce the sidelobes of the calculated range asymmetrically. Specifically, I want the sidelobes at a larger range than the target to have a smaller magnitude than those at a smaller range than the target.

The reason I want to do this is that for a given target, the power received should decrease as $$r^4$$ per the radar equation. The $$r^4$$ factor can be taken to imply that for the same target, my response will decrease -12 dB every time I double my distance from the radar.

This means that if I have a target at 0.25m and 2m of the same size then I would expect the target at 2m to be -36 dB down from the target at 0.25m. In order to push the sidelobes down below -36 dB, I would need to use a pretty aggressive window, and even then, the -36 dB will make it difficult to see targets that are far away and small. i.e., at large ranges, there is likely to be a small dynamic range before my targets have the same magnitude as the side lobe level.

Thank You,

• The Fourier Transform of any real function of time, has Hermitian symmetry in the frequency domain. The magnitude is even symmetry and the phase is odd symmetry. But you could define a main lobe with asymmetric sidelobes and inverse Fourier Transform back to the time domain, and you will get a window function that has complex values. Jan 27, 2023 at 3:41
• This can copy-paste as an answer, OP should create another question about the specific design @robertbristow-johnson Jan 27, 2023 at 11:28
• @robertbristow-johnson yes please paste that as the answer, I think it is sufficient and generally helpful Jan 27, 2023 at 16:50
• If you don't I will!
– Jdip
Jan 27, 2023 at 18:01
• oh, all right. <sheesh> Jan 27, 2023 at 20:06