Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t)...
Consider the RC circuit shown below. Assume that R=(0.1)2 and C=(0.1)F 3. R i(t) y (t) x(t) The input to this circuit is given as x(t) s(t)+ny (t), where the noise component of input, n(t), is a sample function realization of white noise process with an autocorrelation function given by Rpx(t) 8(T), and s (t) cos(6Tt) is the signal component of input. IS(fOI df, where S( a. Find the power of the signal component of input, Ps is the Fourier...
Find the power of the signal conponent of a P is the Fourice t of s,(0)(2.5 points) edf,where S.f density of pu nose (2.5 points) . Consider the RL circuit shown below. Assume that R-10 and L-IN. Hint : Use Parseval's relationship if necessary i(t) e. What is the input signal-o-oise (SNR,ratio, defined as: SNR, 1olog..C)as polnts d. Find the output power spectral density of noise N,00 N,( HP, where HU) is the frequency response of the circuit, and N,(n)...
Q.2 ICO2]10 Marks] The signal g(t) forms the input to the LPF circuit shown in the figure, where R l,and y(Dis the output. If the power spectral density (PSD) of the signal ge) is (a) The autocorrelation of g(t) (b) The 3-dB bandwidth of the LPF (c) The power of g(t) and y(t) (d) Based on your answers above, will it be better if the signal has more or less bandwith? (e) If a white noise of PSD No/2 is...
The input r(t) to a DSBSC receiver is a DSB signal s(t) = A m(t)cos (21fet) corrupted by additive white Gaussian noise with two-sided power spectral density N,/2, where No = 10-12 W/Hz, m(t) is a message signal bandlimited to 10 kHz. Average power of m(t) is Pm = 4 W and Ac = 2 mV. The block diagram of the receiver is shown below. Note that the receiver has filters which have slightly larger bandwidths than a typical DSB...
can you please solve this problem step by step, thank you!! 1. Consider a DSB-SC signal with noise passes through a demodulator shown below. ViC0) 2(0) но но 0) The input signal plus noise is v,(t)-5,() + n'(t) where 5,0): Am(1)cos2r/rt, m(1) cos 2π/J is the message signal with f-</м , carrier frequency is f> fe , and noise n' (r) has power spectral density function G,じ)= η . The local carrier is v,(1)s 2 cosZrw. The carrier filter is...
3. (40 points) A binary communication system transmits signals s (0) (i = 1, 2). The receiver samples the received signal r(t) = s(t)+ n(t) at T and obtain the decision statistic r =r(T) = S(T) + n(T) = a, un, where the signal component is either a = + A or a, = -A with A >0 and n is the noise component. Assume that s (6) and s(l) are equally likely to be transmitted and the decision threshold...
3. The following is the amplitude spectrum of a DSB+carrier AM signal x(f) 1.5 1.5 1.5 1.5 f (Hz) 1920 2000 2080 2080 2000 1920 (a) (10 points) Determine the carrier frequency fe the carrier amplitude Ac the mod ulation index ,, and the message signal m(t) of the AM signal. (b) (10 points) Given that μ2Sm 0.18, find the output SNR (in dB) if the received signal includes white noise with a power spectral density of η/2-10-10 W/Hz. (c)...
3. (30 points) A binary communication system transmits signals s(t) (i 1,2). The receiver samples the received signal r(t) s(t) + n(t) at T and obtain the decision statistic r(T) S (T) n(T) a + n, where the signal component is either an +A or a2-A with A >0 and n is the noise component. Assume that s1 (t) and s2(t) are equally likely to be transmitted and the decision threshold is chosen as zero. If A 1 and the...
Let the signals x(t) and y(t) be the input and output signals to a differentiator, respectively. x(t) do y(t) (a) Let the autocorrelation of the signal x(t) be R (T) and the autocorrelation of the signal y(t) be R (T). If y(t)= X, express R, (T) in terms of R. (T) dt (b) Assume R (T) = 5e and find the power in the output signal y(t). JA, \f}<B (c) Assume that the power spectral density (PSD) of x(t) is...
Consider a FM system that is used to communicate the following message signal: S. m(t) 20 0.05 0.1 015 10 -0.05 with a frequency deviation constant ky 10, and a message bandwidth of W =15 kHz the one-sided noise power-spectral density in the transmission channel is No= 10-8 W/Hz, and an attenuation of 10 is introduced during transmission in the channel as well. a. What is the average-to-peak-power ratio of the message (or, equivalently the power content of the normalized...