(a)
(i)
Determine the transfer function, H(s), of the circuit shown in Figure 3.
R,
V
Figure 3: Electrical circuit
[15%]
(ii)
Show how to construct the linear piecewise Bode amplitude and phase plots if R = 1 k, C = 0.1 F, and the value of R is a value of your choice between 1 k and 10 k. [15%]
(iii)
Sketch both the Bode amplitude and phase plots. Show clearly your workings. 1%071
(b)
Related to signals and Fourier Transform, answer the following
(i)
Let g(t) = sinc^4(x)e^(2ext) dx, find the Fourier Transform of g. [10%]
(ii)
Find the Energy Spectral Density of the following signal. 1%011
(c)
An engineer has designed an amplitude modulation (AM) communication system. When the input signal m(t) is sent to the AM system, it produces the following modulated signal: s(t) = A[D + km(t)]cos(2Ï€fet), where A, D, k, and fe are the AM system parameters. The engineer uses A = 1, D = 0, k = 0.5, and fe = 20000 Hz for the setting. A test has been performed using the message signal where m(t) = cos(60000nt), and distortion has been observed at the receiver.
(i)
Analyze and describe the causes of the distortion and suggest how the system parameters should be adjusted to eliminate the distortion. [20%]
(ii)
If the same message signal is used on a wideband frequency modulation (WBFM) communication system with a frequency deviation of 70 kHz, what is the required channel bandwidth? [%01]
