Reference no: EM132594945

ENG227 Electromagnetics and Communication Technology - Charles Darwin University

Question 1

If a periodic signal has the even-symmetry property v( - t) = v(t), then the Fourier series coefficient can be written as

c_n = 2/T_{0 0}∫^T0/2 v(t) cos(2Πnt/T₀)dt

Use this expression to find c_n when v(t) = A for |t| < T₀/4 and v(t) = -A for T₀/4 < |t| < T₀/2. As a preliminary step you should sketch the wave-form and determine c₀ directly from (v(t)). Then sketch and label the spectrum after finding c_n.

Question 2

Consider the sine pulse v(t) = Asin(2Πt/r)∏(t/T). Show that V(f) = -j(AT/2)[sinc(fτ - 1) - sinc(fτ + 1)1.

Question 3 Find y(t) = v(t) * w(t) for v(t) = Ae^-at for t > 0 and w(t) = Be^-bt for t > 0. Both signals equal zero outside the specified ranges.

Question 4 A given system has impulse response h(t) and transfer function H(b. Ob-tain expressions for y(t) and Y(f) when x(t) = A[δ(t + t_d) - δ(t - t_d)].

Question 5

Find and sketch |H(f|) and arg H(f) for a system described by the differential equation dy(t)/dt + 4Πy(t) = dx(t)/dt + 16Πx(t).