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Question 1. 1. (TCO 1) A sinusoidal signal has an amplitude of 10, frequency of 2 Hz, and initial phase of 60 degrees. It passes through an LTI system and undergoes a gain of 3.5 and a 60-degree phase lag. The resulting output signal will be mathematically described as (Points : 10)

3. (TCO 2) An RLC circuit, with an initial voltage across the capacitor and polarity as marked on the circuit, is shown below. The switch is closed at t = 0 and a current i(t) is assumed to flow clockwise in the circuit. Determine which expression correctly represents the Laplace-transformed value of current, i(s). Note that the coefficient of the highest power of s in the denominator may have to be made unity.
5. (TCO 4) A signal consists of only two sinusoids, one of 35 Hz and one of 45 Hz. This signal is sampled at a rate of 230 Hz. Find the first six positive frequencies that will be present in the replicated spectrum. (Points : 10)

6. (TCO 4) A discrete signal or sequence is given in a table below as a function of n or a sample number. All values not shown can be assumed to be zero. Find the z-transform of the signal. Hint: Use the basic definition of z-transform
7. (TCO 4) A system samples a sinusoid of frequency 1,070 Hz at a rate of 545 Hz and writes the sampled signal to its output without further modification. Determine the frequency that the sampling system will generate in its output. (Points : 10)

Question 8. 8. (TCO 4) A signal has a spectrum from 0–250 Hz as shown below. It is sampled at a rate of 375 Hz. Find the region of the baseband spectrum that will become corrupted and unrecoverable even if an ideal “brickwall” filter is used for recovery.

Question 1. (TCO 7) If our sampling rate is fixed, how can we make the resolution of Fourier transform finer (i.e., be able to resolve frequencies in spectrum that are closer together)? (Points : 10)
Question 2. (TCO 1) Does a sine wave have odd symmetry or even symmetry, and why? (Points : 10) a sine wave has even symmetry since it is smooth and forms periodic wave of 2pie .

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