Reference no: EM131229603
Signal and Systems Assignment-
Problem 1. Topics: Fourier Series Coefficients
a) Give an expression for the periodic waveform; x(t), shown below in the interval [0,1) and [1,2).
b) For the periodic signal shown in the picture find the following Fourier Series coefficients.
Problem 2. Topics: Sinusoidal response of LTI systems
For a certain LTI system; T, the magnitude and frequency response at ω = π/5 are known to be |H(π/5)| = 0 and angle{H(π/5)} = θh(π/5) = 0. It is also known that |H(π/3)| = 1 and angle {H(π/3)} = θh(π/3) = π/4
a) Based on the above information find the steady state output of the system to the input x(t) = 3cos((π/5)t)u(t).
Problem 3. Topics: Exponential Fourier Series Coefficients. Average Power in a periodic signal.
Consider the following periodic signal
a) Find the exponential Fourier Series coefficients.
b) Find the average power of the periodic signal.
Problem 4. Topics: Linear Convolution
Given the discrete-time linear time (shift) invariant system:
where x[n] = δ[n] - δ[n-1] + δ[n-2] - δ[n-3] + δ[n-4] - δ[n-5] + δ[n-6] + δ[n-7]
Using any method find the filter output to this input and write in terms of delayed unit-samples.
Problem 5. Topics: Z-Transform
Find the Z transform of x[n] = - 0.8n-7u[-n+5].
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