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## How Digital Filters Work

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In the preceding chapter we saw how, for digital filtering, the radar returns are translated to video frequencies by a pair of synchronous detectors and sampled at precisely timed intervals. And we learned how the samples are converted to digital numbers. We were told that the numbers are then supplied to a computer (signal processor), which 'forms' a separate bank of doppler filters for each sampling interval (range gate). But little was said about the way in which the filters are formed. In this chapter, we will learn how that is done. After briefly reviewing what the stream of numbers supplied to the computer represents, we will derive the simple set of equations (algorithm) which the filter must repeatedly compute to form a filter - the discrete Fourier transform - and see how the required mathematical operations may be organized. Finally, we will briefly consider what can be done to reduce the sidelobes which invariably occur on either side of a filter's passband. The organization of a complete filter bank and the ingenious approach taken to minimizing the otherwise staggering computing load (the fast Fourier transform) are covered in the next chapter.

Chapter Contents:

• Inputs to the Filter
• What the Filter Does
• Discrete Fourier Transform
• Implementing the DFT
• Sidelobe Reduction
• Filtering Actual Signals

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