Question

+00 k-00 The signal z(t) received by a binary communication system can be expressed as z(t) = axpe(t – kT)+w(t) where ax = £1, an equally likely and independent binary sequence, and w(t) is white Gaussian noise with spectral density S(f)= N, /2. The pulse shape pe(t) is as shown below. a) Write down and sketch the noncausal matched filter impulse response. b) Without making any calculation, make a sketch of the expected filter output wave shape when the input is only the pulse shape pe(t). c) Matched filter output sampling time is adjusted for maximum signal to noise ratio. Obtain the signal and noise powers at the instant of sampling and determine from them the maximum signal to noise ratio. Relate this result to the energy of the pulse pe(t). d) Write down and sketch the impulse response of the causal matched filter having minimum time delay. Pc(t) A 3/6 T t

Answer 1

0 Answer: Given that, The signal (t) received by be expressed as a binary communication system can to z(t) 2 E ak pc (6-kt) + w [t) kece where, QK = El, an white Grassian equally and independent binary sequence, ، ایس noise spedral density ( sw (t)) = Nole a) sktech jen non causal matched filter implause sresponse: s(t) Decision device filter TC inct) noise So Lt) = s()+ A(1) from schwartz Inequality SHIR = si sCf²1df No12 ..(S/N) mar 2E no now, janfth HCH) s(f) e n{t) jo nl) e seoft df ejerft af jo schleierfra UCP) e ** 2jt (16-1) df :.6(1): S (bot)

wave b) Sketching the Expected filter output is only the pluse shape Pelt): shope when the input Let sit) be seal slt) Islot) t 0 filter shape s(-1t -T )) .: to:1 S(T-E) = holt) >t T c) obtain Impluse shape of matched filter the signal and noise powers: no gl H (fyldf now, I SOHCF) 3(4) e úlofto del SNR - wole SIM (F)* df SNR & 15 (1)!-df alo/2 Tilesofts) Ci shume te .° (]* df is energy of plwe felt) d) Pelt) 1 E- - !!* -69371 6). 3 A27 12 QAT 3 no minimum kime delay.

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