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Sidelobes are phenomena encountered often in mathematics and engineering, most often fourier analysis and digital signal processing, as well as antenna design.

Sidelobes are one of the products of a fourier transform operation. Any time-domain waveform of finite duration will contain many frequency components. In the transformed data, there will be main peaks (or lobes) in the locations of the dominant frequencies. Contaminating this data will be sidelobes, which appear directly adjacent to the mainlobe. The sidelobes generally repeat periodically with a exponentially decreasing amplitude envelope.

Sidelobes are generally considered a bad thing. This is because the fourier transform is often used to find the fundamental frequencies of a waveform. Many waveforms can be noisy, which adds other secondary frequencies on top of the fundamental. Perform an FFT, and the sidelobes from all the secondary frequencies can often overwhelm the desired peaks, making them difficult to distinguish or extract.

To combat this, there exists a host of sidelobe suppression techniques. If you are doing basic DSP, using a Hamming Window on your waveform before the FFT will knock the sidelobes way down (with a few side-effects). If you are in need of something a little more clever, you may wish to look into matched filters.

Most antennas are designed to focus most of their radiation in a single direction. As an antenna's radiation pattern is the spatial fourier transform of its excitation currents, it will have sidelobes to some degree. These are unwanted because the radiated energy is going in directions you don't want it to go, or being recieved from a direction you're not aiming the antenna (very important in radar antenna designs). Many antennas are designed using software that will optimize the antenna's shape to reduce the sidelobes as much as possible.

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