Problem 5 Let X(t) be a white Gaussian noise with power spectral density Sxx (w) = No. Assume that X(t) is input to an LTI system with impulse response h(t) = e tu(t). Let the output of the LTI system be Y(t). (a) Find Syy (w). (b) Find Ry (T). (c) Find E[Y(t)²].
Electromagnetic Power Density
The power density of an electromagnetic (EM) wave is proportional to the square of the frequency of electric field (or magnetic field). The moving charge produces both electric field and magnetic field. Electric and magnetic fields are inseparable and exist in combination in EM waves.
Wave Reflection and Transmission
Reflection is defined as a sudden change in the path of the wave that strikes the boundary between two types of media. The least part of the disturbances coming from the wavelength remains the same within the same area. The reflection of the wave takes place by following everyday thinking, simple rules, at the ends of the plane. The coefficient of reflection is the ratio of the amplitude of the reflected wave to the value of the incident wave.
Skin Depth
The wire-type conductors are used in the transmission of electrical energy or signals using an alternating current. The electrons are driven apart due to the electric field created nearby the copper conductor surface. The magnetic field changes with the change in the current density. This change in the magnetic field produces an electric field that opposes the current density change. This electric field is known as back electromotive force (EMF). This force is stronger inside the copper conductor and is weaker at the surface. An alternating current can be induced due to the magnetic field according to the law of induction. Such a current is produced due to the electromagnetic wave impinging on the copper conductor.
Plane wave propagation
Any of the ways how waves travel is known as wave propagation. One can find the difference between longitudinal wave and transverse wave with respect to the direction of oscillation, which is related to the propagation direction. Propagation may occur in vacuum for electromagnetic waves as well as in material medium. Other types of waves need a transmission medium to exist and cannot propagate through the vacuum. The amplitude of a wave is the maximum distance from the displacement of the particle from its resting position on the medium. The waves that propagate are of two types, Pressure waves or Shear waves.
![Problem 5
Let X(t) be a white Gaussian noise with power spectral density Sxx (w) = No. Assume that X(t) is input
to an LTI system with impulse response h(t) =etu(t). Let the output of the LTI system be y(t).
(a) Find Syy (w).
(b) Find Ry (T).
(c) Find E[Y(t)²].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc231fac6-f61a-45b2-b174-05bc9b27b74a%2F487f40a1-7a4f-4d5b-a4cc-f6cf16403a8a%2Fi65esn_processed.jpeg&w=3840&q=75)
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