10) The impulse response of the channel modeled as an LTI system is given as h(t) = 55(t-10). a) Find the transfer function of the system and sketch the amplitude and phase spectrums. b) If the signal x(t) = 10 +10t sinc (t) is applied to the input of the system, what will the output signal be? c) If the input signal is x(t) = 20 cos(2000лt) +10sin (4000лt), find the power spectral density (PSD) of the x(t).

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10) The impulse response of the channel modeled as an LTI system is given as h(t) =
58 (t-10).
a) Find the transfer function of the system and sketch the amplitude and phase
spectrums.
b) If the signal x (t) = 10 + 10t sinc (t) is applied to the input of the system, what
will the output signal be?
c) If the input signal is x(t) = 20 cos(2000nt) + 10sin (4000πt), find the power
spectral density (PSD) of the x(t).
d) If the input signal is x(t) = 20 cos(2000nt) + 10sin (4000nt), find the output
signal y(t) and its PSD function.
e) Find the autocorrelation function of the output signal.
f) Find the output power using both autocorrelation function and PSD function.
Transcribed Image Text:10) The impulse response of the channel modeled as an LTI system is given as h(t) = 58 (t-10). a) Find the transfer function of the system and sketch the amplitude and phase spectrums. b) If the signal x (t) = 10 + 10t sinc (t) is applied to the input of the system, what will the output signal be? c) If the input signal is x(t) = 20 cos(2000nt) + 10sin (4000πt), find the power spectral density (PSD) of the x(t). d) If the input signal is x(t) = 20 cos(2000nt) + 10sin (4000nt), find the output signal y(t) and its PSD function. e) Find the autocorrelation function of the output signal. f) Find the output power using both autocorrelation function and PSD function.
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