Final answer:
The output of an LTI system with the given frequency response function H(ω)=1/(jω+3) is computed for various inputs by applying concepts like DC input, convolution, and Fourier Transforms.
Step-by-step explanation:
A student has asked how to compute the output of an LTI (Linear Time-Invariant) system given its frequency response function H(ω)=1/(jω+3) and various inputs.
- (a) With a constant input x(t)=3, the output is also a constant since a DC input through any stable system stays constant, hence y(t)=3.
- (b) For x(t)=32cos(3t), we calculate the Fourier Transform, apply the frequency response, and then perform the inverse Fourier Transform to find y(t).
- (c) For x(t)=5cos(4t), similar steps as (b) are taken.
- (d) For an input of δ(t), the output is simply the system's impulse response: y(t)=H(t).
- (e) For the unit step function u(t), we need to calculate the convolution of H(t) and u(t) to get y(t).
- (f) With a constant input x(t)=1, like in (a), the output is also constant: y(t)=1.
Each case requires using the properties of LTI systems and incorporating terms like frequency response, convolution, DC input, impulse response and Fourier Transform.