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An LTI system has the frequency response function H(ω) = 1/(jω + 3). Compute the output if the input is

a. x(t) = 3
b. x(t) = 3√2 cos(3t)
c. x(t)= 5cos(4t)

User Jmpena
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Final answer:

The output of an LTI system with a given frequency response function can be computed for various inputs, including constants and sinusoidal functions, by applying the system's frequency response to the inputs.

Step-by-step explanation:

The subject of this question is related to an LTI system (Linear Time-Invariant system) in the field of Engineering, specifically dealing with signals and systems. Given the frequency response function H(ω) = 1/(jω + 3), we are asked to compute the output if the input is three different signals. The computations are based on the fact that in LTI systems, the output to a sinusoidal input can be determined using the frequency response function of the system.

For a constant input x(t) = 3, the output will also be a constant, since the system is linear.

For inputs that are sinusoidal such as x(t) = 3√2 cos(3t) and x(t) = 5 cos(4t), the output is found by multiplying the input by the system's frequency response at the input frequency.

User Doughy
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