Answer Happy

I Problem 1: We want to transmit a random binary digital signal whose bit rate is 10 kbits/sec via a channel where an additive white Gaussian noise is added. We have a basic pulse form p(t) of duration T = 0.2ms, which means that the pulse has a length of 2 bits. A '1' bit is represented by p(t) and a '0' bit by-p(t). Moreover, the pulse p(t) has the following form: p(t) T a) If g(t) is a square pulse between -and and of amplitude √A, then p(t) can be obtained by convolving g(t) with itself, i.e., p(t) = g(t) + g(t). Knowing that the Fourier transform of a square pulse, centered on 0, of amplitude 1 and width T is given by : w (t) = rect (7) W(S) = 7 sin(2/1). • Determine the Fourier transform P(f) of the pulse p(t): -Tsinc(fT).
b) Determine the mathematical expression for the power spectral density of the transmitted signal. c) This signal is passed through a low pass filter to the gain receiver |H(f)| = 1.5 in the passband and whose cut-off frequency is fc = 5kHz. Determine the output noise power if the bilateral noise power spectral density in the channel is 1μW/Hz. d) In your opinion, does the passage of the signal through the low-pass filter described in (c) allow it to be detected correctly at the receiver? Explain.