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For the Radar Case: The bandwidth of the pulse is the reciprocal of the Pulse Duration (called Pulse Width) as any filtering needs to be able to detection and follow the pulse shape and its edges. The pulse width is the AM modulation to a Fixed Frequency Carrier Frequency and the AM modulation will be greater bandwidth then the Carrier Frequency. As you are attempting to reject receiving other emissions and noise that do not match your own emissions such that your receiver is "match filtered" to your emissions, your receiver bandwidth will be at least the reciprocal of the pulse width but is lightly to be a smaller bandwidth then the reciprocal of the pulse width.

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