In signal processing, the design of many filters can often be cast as a constrained optimization problem where the constraints are defined by the specifications of the filter. These specifications can arise either from practical considerations or from the standards set by certain regulatory bodies. Traditional filter design techniques are developed in the frequency domain where the response of a filter at a particular frequency is dependent solely on the excitation of that frequency. This is not true with time domain problems. Clearly, an excitation applied at any time will have effects on the response at all times after the application of the excitation. Conversely, the response at any particular instant depends on all the excitations that have been applied to the filter prior to that instant. This difference manifests mathematically in the form of multiplication and convolution.
KeywordsImpulse Response Pulse Shape Finite Impulse Response Matched Filter Pulse Compression
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