A digital communication system uses the signals si(t) and s2(t) shown in Fig. 1 to t equally like...
Problem 1: A baseband digital communication system employs the signals shown below (Figure 1) for transmission. The channel has no attenuation and the noise is AWGN with power-spectral density NO/2. The probability of transmitting sı(t) is twice that of sz(t). S1() T12 O TV2 T Figure 1 2 a) Find an appropriate orthonormal basis for the representation of the signals. 7 b) Plot the constellation diagram in term of average symbol power. c) Draw the decision regions assuming equally likely...
here is the solution for the question but i need someone help to understand part b please. ф1(t) 2(t) 0. -1 Figure 7: Set of orthonormal basis functions in Problem 4 The signals si(t) and s2(t) are given by 201 (t) +dy(t) s2(t) h2(t) hi(t) (a) Design and draw the matched filter for the system using the above orthonormal basis functions to minimize the BER Result is in Fig. 8. (b) Design and draw the receiver for the system using...
Problem 4 A base-band digital communication system using binary signals shown in the Figure for transmission of two equiprob able messages. The transmitted signal is s(t), i e {1,2} and the recieved signal is r(t) s(t)+n(t), where nit) is the AWGN with power-spectral density No/2. 1. In a block diagram, give the precise specifications of the optimal receiver. What are the characteristics of the matched filter and the sampler and decision device? 2. Find the error probability of the optimal...
show steps 7 pts) Consider an FSK system where bits 1 and 0 are transmitted using signals si(t) and s2(t) 2Eb 2Eb where θ1 and 02 are the phases of the two signals. (a) (3 pt) Find the correlation between the signal s1(t) ard salt), i.e., find oin(t)s2(t)dt. b) (2 pt) Assuming non-coherent carriers, i.e., θ|メ02, state the condition for which the correlation derived in part (a) goes to zero. (c) (2 pt) Repeat part (b) for the case where...
2. (30 marks] Consider the system shown in Fig. 1. Find the output y(t) for the following h(t) and r(t) using the convolution integral. x(r) y(r) h(t) Figure 1: System for Q2 1.5 2t33 0 otherwise h(t)=2rect(-3.5) x(t) = h(t) = 2 rect (-3 -
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input.x is used for signal transmission to produce the channel output y,i.e., r- x . Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2(r) in Fig.2 decisions 22(r) Figure 1. A channel with the input x and output r corrupted...
1. Consider the system shown in the figure below. The system is an integrator, in which the output is the integral: y(t)x()dr -00 Integrator x(t) y(t) (a) We may determine the impulse response h(t) by applying an impulse signal to the integrator, i.e. x(t) -5(t). What is the impulse response? Answer: (10 points) (b) The output of the integrator may be found by apply convolution method to determine the output. The convolution of the two signals is expressed a)ht -...
24-8 An LTIC system has impulse response ho shown in Fig. P2.4-8. Lett have units of second Let the input be x(1) = u(-1-2) and designate the output as yzsr(t) = x(t) *h(t). (a) Use the graphical convolution procedure where h(t) is flipped and shifted to deter- mine yzsr(t). Accurately plot your result. (b) Use the graphical convolution procedure where x(1) is flipped and shifted to deter- mine Yzsr(t). Accurately plot your result. -2 -1 0 1 2 3 4...
8. Determine the natural frequencies of the system shown in Fig 1, where fi (t) = falt) = 0 and 1c 0. The resulting equation of motions are: xi(t) 2(t) k1 m1 m2 C3 Figure 1: 2 DOF system