Signal Processing - Study Mode
[#86] Consider a random sinusoidal signal x(t) = sin(ω 0 t + φ), where a random variable 'φ' is uniformly distributed in the range $$ pm frac{pi }{2}.$$ xa0The mean value of x(t) is
Correct Answer
(B) $$frac{2}{pi }$$ sin (ω 0 t)
[#87] Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a k } be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t): 1. The complex Fourier series coefficients of x(3t) are {a k } where k is integer valued. 2. The complex Fourier series coefficients of x(3f) are {3a k } where k is integer valued. 3. The fundamental angular frequency of x(3t) is 6π rad/s. For the three statements above, which one of the following is correct?
Correct Answer
(B) Only 1 and 3 are true
[#88] Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are
Correct Answer
(A) 5 Hz and 15 Hz only
[#89] The Fourier transform of y(2n) will be
Correct Answer
(C) e -jω [cos2ω + 2cosω + 2]
[#90] The Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it is odd S. Sine terms if it is odd Which of the above statements are correct?
Correct Answer
(A) P and S