71. Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} 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 {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} 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?
1. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} 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?
72. 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
73. Consider a four point moving average filter defined by the equation $$y\left[ n \right] = \sum\nolimits_{i = 0}^3 {{a_i}x\left[ {n - i} \right]} .$$ The condition on the filter coefficients that results in a null at zero frequency is
74. The Fourier transform of y(2n) will be
75. 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?
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?
76. For a function g(t), it is given that
$$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .
$$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .
77. A linear discrete-time system has the characteristics equation, z3 - 0.81 z = 0. The system
78. A function is given by f(t) = sin2t + cos 2t. Which of the following is true?
79. Two systems H1(z) and H2(z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H2(z) is
$$x\left( n \right) \to \boxed{{H_1}\left( z \right) = \frac{{\left( {1 - 0.4{z^{ - 1}}} \right)}}{{\left( {1 - 0.6{z^{ - 1}}} \right)}}} \to \boxed{{H_2}\left( z \right)} \to y\left( n \right)$$
$$x\left( n \right) \to \boxed{{H_1}\left( z \right) = \frac{{\left( {1 - 0.4{z^{ - 1}}} \right)}}{{\left( {1 - 0.6{z^{ - 1}}} \right)}}} \to \boxed{{H_2}\left( z \right)} \to y\left( n \right)$$
80. Consider the z-transform X(z) = 5z2 + 4z-1 + 3; 0 < |z| < ∞. The inverse z-transform x[n] is
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