STUPIDSID
1 (a)
Determine whether the following signals are energy or power signals. Calculate their energy or power.
(i) x[n] = u[n]
(ii) x(t) = Asin(t) ; -∞ < t < ∞
(i) x[n] = u[n]
(ii) x(t) = Asin(t) ; -∞ < t < ∞
4 M
1 (b)
State and prove the following properties of Fourier Transform(i) Time Shifting.
(ii) Differentiation in time domain.
(ii) Differentiation in time domain.
4 M
1 (c)
Check whether the following systems are linear or non-linear, time-invariant or time-variant, causal or non-causal, static or dynamic -
(i) y(t) = x(t) cos(100πt)
(ii) y(t) = x(t + 10) + x2(t)
(i) y(t) = x(t) cos(100πt)
(ii) y(t) = x(t + 10) + x2(t)
4 M
1 (d)
Compare Discrete time Fourier Transform and Continuous Time Fourier Transform.
4 M
1 (e)
State and discuss the properties of Region of Convergence for Z-Transform.
4 M
2 (a)
Determine the exponential form of Fourier Series representation of the signal shown
10 M
2 (b)
Determine whether the following signals are periodic or non-periodic. If periodic, find the fundamental period.
(i) x(t) = cos(t)+ sin(√2 t)
(ii) x(t) = sin2t
(iii) x[n] = cos[n/2]
(iv) x[n] = cos2[πn/8]
(i) x(t) = cos(t)+ sin(√2 t)
(ii) x(t) = sin2t
(iii) x[n] = cos[n/2]
(iv) x[n] = cos2[πn/8]
10 M
3 (a)
The analog signal given below is sampled at 600 samples per second
x(t) = 2sin(480πt) + 3sin(720πt)
Calculate:
(i) Minimum Sampling rate to avoid aliasing.
(ii) If the signal is sampled at Fs=200Hz, what is the discrete time signal after sampling?
(iii) If the signal is sampled at Fs=75Hz, what is the discrete time signal after sampling?
x(t) = 2sin(480πt) + 3sin(720πt)
Calculate:
(i) Minimum Sampling rate to avoid aliasing.
(ii) If the signal is sampled at Fs=200Hz, what is the discrete time signal after sampling?
(iii) If the signal is sampled at Fs=75Hz, what is the discrete time signal after sampling?
10 M
3 (b)
Determine the DT sequence associated with Z-Transform given below -
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10 M
4 (a)
Draw Cascade and Parallel Realization. The transfer function of discrete time causal system is given by
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10 M
4 (b)
Obtain the convolution of
x(t) = u(t) and h(t) = 1 for -1 ≤ t ≤ 1
x(t) = u(t) and h(t) = 1 for -1 ≤ t ≤ 1
10 M
5 (a)
Obtain the inverse Laplace Transform of
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10 M
5 (b)
Find the Fourier Transform of:
(i) e-2(t-1)u(t-1)
(ii) x(t)=|t|
(i) e-2(t-1)u(t-1)
(ii) x(t)=|t|
10 M
6 (a)
Determine the impulse response of DT-LTI system described by the difference equation (for n≥0)
y[n] - 0.5y[n-1] = x[n] + (1/3)x[n-1]
where all the initial conditions are zero.
y[n] - 0.5y[n-1] = x[n] + (1/3)x[n-1]
where all the initial conditions are zero.
10 M
6 (b)
A causal LTI system has a Transfer Function H(z) = H1(z) H2(z) where
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(i) If system is stable, give ROC condition.
(ii) Find the impulse response.
(iii) Find system response if X(z) = 1/(1-0.2z-1)
(iv) Draw pole-zero diagram.
(i) If system is stable, give ROC condition.
(ii) Find the impulse response.
(iii) Find system response if X(z) = 1/(1-0.2z-1)
(iv) Draw pole-zero diagram.
10 M
7 (a)
Using suitable method obtain the state transition matrix for the system matrix
10 M
7 (b)
The transfer function of the system is given as
Obtain the state variable model.
Obtain the state variable model.
10 M
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