14. Given sequence x= [4.74, 7.38, 7.74, 2.44, 1.16, 6.11*, 9.77, 0.04, 8.48, 1.75] which sample is found at the sample index n = 3 ?
(a) 7.74 (b) 8.48 (c) 2.44 (d) 1.75
15. A discrete signal x(n)={ -1*,1} is correlated (not convolved!) with the sequence y(n)={ 2*,0,1 } to give the sequence z(n)=x(n) corr y(n) in this order. What is the sequence z(n)?
(a) {1,-2,3,-1} (b) {-1,1,-2,2} (c) {1,-2,0,-1} (d) {2,-2,-1,1}
16. Given two arbitrary row vectors x and y of length N, which Matlab expression will make a scalar?
(a) x. * y (b) x * y (c) y * x' (d) x' * y
17. Let x=2-0j and y=1-1j and then quotient x/y is
(a) 2 + 2j (b) 1 + 1 j (c) ½ - ½ j (d) 1 - 1j
18. A sine wave which has a zero-crossing of the time x-axis every 10^-6 seconds has frequency of
(a) 1/2 MHz (b) 1 MHz (c) 50 KHz (d) 1 KHz (Note: K=10^3, M=10^6, G=10^9)
19. The angular frequency ̐ above which there are no frequencies in the Fourier transform of the signal x(t) is called the
(a) sampling frequency (b) bandwidth (c) Nyquist rate (d) spectrum
20. A complex vector Z has magnitude 29 and is represented by the complex point (20, Y). Y is equal to
(a) 21 (b) 41 (c) 25 (d) 18
21. What is the sum of the infinite series (1 - 1/5 + 1/25 - 1/125 ....) ?
(a) 2/3 (b) 5/6 (c) 11/15 (d) 8/10
22. The sum of two phasors √2 ∠ 45° and √2 ∠ 315° is
(a) 2 ∠ π/4 (b) √2 ∠ π/8 (c) 2 ∠ 0 (d) 2√2 ∠ π/2 Note: sin(θ)=cos(θ-90°)
23. The unit step sequence of s(n)=u(n-3)-u(n-6) is the same as the sequence
(a) [1,1,1,1*,1,1,1,1,1] (b) ones(3,6) (c) [δ(n-3) : δ(n-6)] (d) Σ k=5 k=3 δ(n-k)
24. The LTI system described by the difference equation y(n)= 2x(n) - 3x(n-2) + 2y(n-1) – y(n-3) has an input given by the arbitrary finite sequence x(n). The vectors a and b for use in Matlab's filter equation y = filter(b,a,x) used to get the output sequence y(n) are
(a) a=[1,2,-3], b=[2,0,-1] (b) a=[1,-2,0,1], b=[2,0,-3]
(c) a=[1,2,0,-1], b=[1,0,-2] (d) a=[1,2,-1], b=[2,-3]
25. A signal is sampled at a rate of fs=10^3 Hz. If the analog linear frequency F associated with a signal is F=250 Hz, then what is the corresponding digital angular frequency ω expressed in radians/sample?
(a) 2.5π x10^-3 (b) 0.25 π (c) 0.25π x10^-3 (d) 0.50 π