Ee 3002 signal and systems fall 2016 assignment exponential

Question

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)} = θ_h(π/5) = 0. It is also known that |H(π/3)| = 1 and angle {H(π/3)} = θ_h(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] = - 0.8^n-7u[-n+5].