STUPIDSID
1 (a)
Determine whether following signals are energy signal or power signal? Calculate their energy of power.
(i) x(t)=A cos (2? f0 t+0)
(ii) x[n]=[1/4]n u[n]
(i) x(t)=A cos (2? f0 t+0)
(ii) x[n]=[1/4]n u[n]
4 M
1 (b)
Determne whether following signals are periodic or non periodic? If periodic find fundamental period.
(i) x(t)=5 cos(4?t)+3 sin(8 ? t)
(i) x(t)=5 cos(4?t)+3 sin(8 ? t)
4 M
1 (c)
Check whether following systems are linear or nonlinear, Time-Invariant or Time variant, casual or non casual.
(i) y(t)=x(t).cos 100 ? t
(ii) y(n)=x(n)+n?x[n+1]
(i) y(t)=x(t).cos 100 ? t
(ii) y(n)=x(n)+n?x[n+1]
4 M
1 (d)
Find the fourier value X(0) and value X(?) of following :
\[x\left(z\right)=\frac{1}{1+2z^{-1}-3z^{-2}}\]
\[x\left(z\right)=\frac{1}{1+2z^{-1}-3z^{-2}}\]
4 M
1 (e)
Find the fourier Transform of double sided exponential signal.
4 M
2 (a)
Determine the exponential from of fourier series representation of signal show in fig 2?1 Hence determine the trignometric from of fourier series.
10 M
2 (b)
(i) Plot the signal with respect to time.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)-u(t-4)-2u(t-5)
(ii) Find the even and odd of this signal.
x(t)=u(t)-r(t-1)+2r(t-2)-r(t-3)-u(t-4)-2u(t-5)
(ii) Find the even and odd of this signal.
10 M
3 (a)
Obtain the fourier Transform of periodic gate function of amplitude A, period To and width t as shown in fig 3?1. Plot the magnitude spectrum.
10 M
3 (b)
State and prove following properties of Fourier Transform.
(i) Convolution in Time domain
(ii) Different in Time domain
(i) Convolution in Time domain
(ii) Different in Time domain
6 M
3 (c)
Explain Gibb's phenomenon.
4 M
4 (a)
An analog signal.
xa(t)=sin[480 ?t]+3sin(720 ?t) is sampled 600 times per second
(i) Determine the Nyquist sampling rate for xa(t).
(ii) Determine the folding frequency.
(iii) What are the frequencies, in radians, in resulting discrete time signal x(n).
(iv) If x(n) is passed through an ideal D/A converter, what is the reconstructed signal Ya(t). ?
xa(t)=sin[480 ?t]+3sin(720 ?t) is sampled 600 times per second
(i) Determine the Nyquist sampling rate for xa(t).
(ii) Determine the folding frequency.
(iii) What are the frequencies, in radians, in resulting discrete time signal x(n).
(iv) If x(n) is passed through an ideal D/A converter, what is the reconstructed signal Ya(t). ?
10 M
4 (b)
Determine the laplace transform of the signals shown in fig 4?1 and fig 4?2.
Fig 4(1)
Fig. 4(2)
6 M
4 (c)
Determine the laplace transform of following using properties of laplace transform. X(t)=(t2-2t)u(t-1).
4 M
5 (a)
Determine the z-transform and sketch R.O.C.
(i) x1[n]=[1/3]n; n ?0
(ii) x2[n]=x1[n+4]
(i) x1[n]=[1/3]n; n ?0
(ii) x2[n]=x1[n+4]
8 M
5 (b)
Determine th convolution of following pairs of signals by means of z-transform.
\[x_1\left[n\right]={\left[\frac{1}{4}\right]}^n\ u\left[n-1\right]\]
\[x_2\left[n\right]=[1+{\left(\frac{1}{2}\right)}^n\ u(n)\]
\[x_1\left[n\right]={\left[\frac{1}{4}\right]}^n\ u\left[n-1\right]\]
\[x_2\left[n\right]=[1+{\left(\frac{1}{2}\right)}^n\ u(n)\]
8 M
5 (c)
Explain properties of region of convergence[R.O.C.] of z-transform.
4 M
6 (a)
The different equations of system is given by-
y(n)=3y[n-2]+4y[n-1]+x[n]
If x[n]=[0.5]n u[n] and
y[-1]=1, y[-2]=0
Find (i) zero Input Response
(ii) zero state Response
(iii) Total Response.
y(n)=3y[n-2]+4y[n-1]+x[n]
If x[n]=[0.5]n u[n] and
y[-1]=1, y[-2]=0
Find (i) zero Input Response
(ii) zero state Response
(iii) Total Response.
10 M
6 (b)
A system is describe by following difference equation.
y[n]=1/2 y(n-1)+1/4 y(n-2) + x(n)+x(n-1)
Obtain
(i) Direct form I Realization
(ii) Direct form II Realization (iii) Cascade Realization
y[n]=1/2 y(n-1)+1/4 y(n-2) + x(n)+x(n-1)
Obtain
(i) Direct form I Realization
(ii) Direct form II Realization (iii) Cascade Realization
10 M
7 (a)
LTI system is characterized by system function-
\[H\left(z\right)=\frac{3-4z^{-1}}{1-3.5z^{-1}+1.5z^2}\]
Specify R.O.C. of H(z) and determine h(n) for
(i) System is stable
(ii) System is casual.
\[H\left(z\right)=\frac{3-4z^{-1}}{1-3.5z^{-1}+1.5z^2}\]
Specify R.O.C. of H(z) and determine h(n) for
(i) System is stable
(ii) System is casual.
8 M
7 (b)
Using a suitable method obtain the state transition matrix eAt for the following system.
\[A=\left[\begin{array}{cc}-12 & \frac{2}{3} \\-36 & -1\end{array}\right]\]
\[A=\left[\begin{array}{cc}-12 & \frac{2}{3} \\-36 & -1\end{array}\right]\]
8 M
7 (c)
Find relationship between Discrete Time fourier transform and z-transform.
4 M
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