. Airborne radar. Airplanes; Guided missiles. 5-10] APPLICATION TO ANALYSIS OF MATCHED FILTER RADAR 277 to and depend upon the wave shape of the signal. For the detection prob- lem, though, it is the received energy that counts. As a concrete illustration of a matched filter, suppose that the signal waveform consists of a series of n identical pulses separated by a repetition period T. Such a signal is of common occurrence in radar problems. Denoting an individual pulse by /)(/), the signal is defined by Pulse train - s{t) =!]/>(/- kT). 0 This signal is depicted in Fig. 5-15a. (5-126). Fig.
. Airborne radar. Airplanes; Guided missiles. 5-10] APPLICATION TO ANALYSIS OF MATCHED FILTER RADAR 277 to and depend upon the wave shape of the signal. For the detection prob- lem, though, it is the received energy that counts. As a concrete illustration of a matched filter, suppose that the signal waveform consists of a series of n identical pulses separated by a repetition period T. Such a signal is of common occurrence in radar problems. Denoting an individual pulse by /)(/), the signal is defined by Pulse train - s{t) =!]/>(/- kT). 0 This signal is depicted in Fig. 5-15a. (5-126). Fig. 5-15a Pulse Train Signal. Envelope = P(co) ^^ T"~-^>^ (Width of spectral teeth - 27r/4fr) .aJ \^^ L^Al'x? 0 ^H 27r/fr Fig. 5-15b Spectrum of Pulse Train Signal. From Equation 5-125, the signal component of the filter output at the observation time will be Filter output (signal) = So{t^ = / s-{T)dj (5-127) E £V(r - kT)p{T - mT)dr 0 0 ^iLp'ir - kT)dT 0 = n\ p''{j)dr. The effect of the correlation (or filtering) operation has been to select out all the available signal pulses and add them together. A device which will perform this addition is most often referred to as a pulse integrator, and. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Povejsil, Donald J. Princeton, N. J. , Van Nostrand
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