Show that the energy content of a signal is equal to the energy content of its Hilbert transform.
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Show that the energy content of a signal is equal to the energy content of its...
Show that a signal and its Hilbert transform are orthogonal.
1. The above two plots show a sinusoidal signal and its spectral content respectively. What is the frequency of the sine wave (and in what units)? 2. What is the largest sampling period (in seconds) that could be used without aliasing for the signal provided. Explain how you obtained the answer. Signal: y-sin(2rft) 0.8 0.6 0.4 ? 0.2 0.2 0.6 0.8 t - [seconds] 25 Spectral Density: IY(fl 20 15 10 Frequency -1?]
1.2-4 For an energy signal x(t) with energy Ex, show that the energy of any one of the signals –x(t), X(-t), and x(t - T) is Ex. Show also that the energy of x(at) as well as x(at - b) is Ex/a, but the energy of ax(t) is a Ex. This shows that time inversion and time shifting do not affect signal energy. On the other hand, time compression of a signal (a > 1) reduces the energy, and time...
(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2 x 103Joules). The signal ra(t) is sampled at a rate of 500 samples/sec to yield its discrete-time counter part (n) (a) Find ti, and hence sketch ra(t). (b) From part (a), plot r(n) and finds its energy (c) Derive an expression for the Fourier transform of a(n), namely X(ew). (d) Plot the magnitude spectrum (1X(e)) and phase spectrum 2(X(e). (e) Consider the signal y(n)...
Power Spectral Density of Signal A signal s(t) can be expressed as the following equation: L-1 where L is a positive integer. {An}n=0 are independent and identically distributed (i.i.d.) discrete random variables. The probability mass function (PMF) of An is An() 0 otherwise, where A is a positive constant in volt. To is a uniformly distributed random variable with probability density function (PDF) defined by 0. otherwise. L-1 To and {An}n=d are independent. The signal p(t) is a pulse and...
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a
3(20%) Assume a message signal is given by m(t) = 4 cos(2π//) + cos(4π.t). Let x (t)-5m(t) cos(2t f t) + 5m(t) sin( 2 fct), where m(t) İs the Hilbert Transform of m(t). (10%) (a) Derive x(t) (10%) (b) Prove, by sketching the spectra, that x(t) is a lower-sideband SSB signal of m(t). 3(20%) Assume a message signal is given by m(t) = 4 cos(2π//) + cos(4π.t). Let x (t)-5m(t) cos(2t f t) + 5m(t) sin( 2 fct), where m(t)...
Please answer clearly and show all steps. I will give it a LIKE. Energy Content You have a kilogram of coal available. a. How much energy content does it contain in J and kWh? b. How high could you theoretically lift 1 litre of water with this energy? c. To what speed (in km/h) could you theoretically accelerate a car (mass: 1 t) with this energy?
3(20%) Assume a message signal is given by m(t) = 4 cos(2π//) + cos(4π.t). Let x (t)-5m(t) cos(2t f t) + 5m(t) sin( 2 fct), where m(t) İs the Hilbert Transform of m(t). (10%) (a) Derive x(t) (10%) (b) Prove, by sketching the spectra, that x(t) is a lower-sideband SSB signal of m(t).
A signal f(t) has a Fourier transform given by Iw+3)-H(W-3)). Use Parseval's theorem to find the total energy content of the signal. Your answer can be expressed as a number accurate to five decimal places or as an expression in correct Maple syntax. For example: 0.1909859317 OR rounded to 0.19099 OR 3/5/Pi Skipped