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). 







This signal is depicted in Fig. 5-1 5a. 



(5-126) 



Fig. 5-1 5a Pulse Train Signal. 



Envelope = P(co) 



^^ 



T"~-^>^ (Width of spectral 



teeth - 27r/4fr) 



.aJ \^^ L^Al'x? 



^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 







^iLp'ir - kT)dT 







= 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 



