SS Tutorial

Aditya Engineering CollegeAditya Nagar,ADB Road, Surampalem

Department of Electronics and communication Engineering

SUBJECT: SIGNALS AND SYSTEMS

UNIT-ITUTORIAL SHEET NO:1

1. Evaluate the following integralsa. b.

2. Add the given signals x1(t),x2(t) and subtract also.

3. Find whether the following signals or periodic or not?

a. x(t)=2 cos (10t+1)-sin(4t-1).b. X(t)=cos60t+sin50t.

4. Determine power and RMS value of following signals.

a. X1(t)=5 cos (50t+/3)b. 10sin (50t+/4)+16 cos(100t+/3)

5. is energy(or) power signal?

Name of the faculty: Signature:



SUBJECT: SIGNALS AND SYSTEMSUNIT-I

TUTORIAL SHEET NO:2

1. Signals are casual or non-casual?

2. Check whether following system isa. Static or dynamicb. Linear or non-linearc. Casual or non-casuald. Time variant or time invariant

3. show that functions sinn0t,sinm0t are orthogonal over

m=n.

4. Split the signals X(t)=et into even and odd parts. Show that they are orthogonal over the interval(-a,a) for arbitary “a”.

5. Prove that are orthogonal.




SUBJECT: SIGNALS AND SYSTEMSTUTORIAL SHEET NO:3

UNIT –II

1.Find the Fourier series for the periodic signal

2. Find the trigonometric Fourier series representation for the periodic signal x(t) as shown in the figure.

3. Find the cosine Fourier series for the half wave rectified sine wave.

4. Compute the Exponential Fourier series for the following signal.

5. Find the average power of the signalsa) x(t)=2 sin2(2500t) cos (20000t) b) y(t)= cos(20000t)-1/2 cos(15000t)




SUBJECT: SIGNALS AND SYSTEMSTUTORIAL SHEET NO:4UNIT –II

1..Find the Fourier series of the periodic signal x(t)=t and repeats every second.

2. Find the exponential Fourier series for the given function.

3. Find the exponential Fourier series for the cosot+ sin2ot

4 A wave form generators produce the square wave x(t) . Find the complex exponential series.

5.. Find the exponential Fourier series of the f(t)= e2t over the interval (0,1).





TUTORIAL SHEET NO:5UNIT –III

1.Find the fourier transform of the e-atu(t) and sketch the magnitude and phase spectrum.

2. Find the inverse fourier transform of the X(j)=(-o)

3.. Find the fourier transform of x(t)= cosot and sinot

4. Find the fourier transform of x(t)= e-3t( u(t+2)-u(t-3)).

5. Find the fourier transform of the single symmetric gate pulse.





TUTORIAL SHEET NO:6

UNIT –III

1. Fin the Fourier transform of the single cosine wave at t=0.

2. Find the Fourier transform of the equidistance impulses of unit strength separated by ‘t’ seconds.

3.Find the fourier transform of the [ 1/ e-t/ u(t).]

4. Find the response voltage in the network shown below using Fourier transforms.

5. Find the fourier transform opf the function f(t)= e-j2t x(t-3), given X(j)= 6/(4+ j)





UNIT-IVTUTORIAL SHEET NO:7

1.Consider a system ‘s’whose input x(n) and output y(n) are related by y(n)=n.x(n). Determine linearity.

2.Check the following sequence for linearity y[n]=cos[s(n)].

3.Test the system linearity, time invariant and causality for the following expression

Y(n)=5n[s(n)]2.

4.Consider a stable system characteristic differntial equation

Find its impulse response and transfer

function?

5.A stable LTI system characterized by the differential equation

find impulse response.





TUTORIAL SHEET NO:8

1.Let the system function of a LTI system response 1/j+2. What is the output of the system for an input (0.8)tu(t).

2.Find the impulse response of the RL filter.

3.Explain poly-wiener creation and conclusions?

4.Test the system linearity,time invariant and casuality fory(v)=kx(n),where x(n)=[x(n+1)-x(n)].

5.Show that the rise time response of an RC LPF .





TUTORIAL SHEET NO:9

1.Find graphically the convolution of f1(t) with a pair of impulses of strength k each.

2.Solve the follwing y(t)= x(t)*h(t).where h(t)=r(t), and x(t)= u(t)-u(t-4).

3.Convolve the following signals

4.Find the response of the system to an input of x(t)=2u(t-10) if h(t) =sin (2t) u(t)

5.A linear time invariant system has the following impulse response h(t) =2.e-at u(t)





TUTORIAL SHEET NO:10UNIT-V

1.B Determine y(t)=x(t)*h(t) where x(t)=u(t) and h(t) is shown.

2.A signal is passed through an ideal LPF with cutt off frequency 1 radian per second . Find the energy density spectrum of the output of the filter.

3.Explain how a noisy signal mixed with a periodic signal can be examined by correlation?

4.Find the mean square power levels and sketch the power density spectra of the following (a) A cos 200t cos 2000t (b) (A+ sin 200t) cos 2000t

5.Find the cross correlation and auto correlation of the following signals.





TUTORIAL SHEET NO:11UNIT –VI1. The signal v(t)= cos5t + 0.3 cos10t is instantaneously sampled . Determine the maximum interval of sampling.

2.The spectral range of a function extends from 10 MHz .. Find the maximum samplin time required for sampling.

3. Consider a signal where maximum input frequency is 5 kHz. Determine the minimum sampling rate for 5 khz signal were allowed to enter the sample and hold circuit.

4. The signal x(t)= 4 + 8 cos8t) is sampled at a rate of 16 samples/sec. Plot the amplitude spectrum of the sampled signal showing the weight and the frequency of each component for f 40Mhz. How can the signal be reconstructed from the samples?

5. State and prove sampling theorem





TUTORIAL SHEET NO:12

1. The signal x(t) = 10 cos (10t) is sampled at a rate of 8 samples/second. Plot the amplitude spectrum for 30 Can the signal be recovered from the samples? Explain.

2. A signal x(t)= sinc(150t) is sampled at a rate of (a) 100 hz (b) 200hz (c) 300hz. For each case can you recover the signal from the sampled signal?

3 Draw Xs(j when xs(t)= x(t) T(t) with the sampling period T where T(t)= (t-nT) for all n.

4. Determine the nyquist rate and nyquist sampling interval for sinc2 (200t)

5. A signal whose spectrum is shown in figure below. Is sampled at a rate of 300 samples/sec. What is the spectrum of sampled discrete time signal?





UNIT –VII TUTORIAL SHEET NO:13

1 Find the Laplace transform and ROC of the following signals(a) e-atu(t) (b) eatu(t) (c) e-atu(t)coso t (d) e-atu(t)sino t

2 Find the laplace transform of e-bt

3 Find the laplace tranform of t2 e-2tu(t)

4. Find the laplace transform of the signal x(t)= sin(t); 0t1 = 0 ; otherwise.

5. Find the Laplace transform of the signal x(t) = e-2tsin2t u(t)






1 Find the laplace transform of the following wave form.

2. Determine the initial value of the following function(a) X(s)= 3/(s2+5s-1) (b) X(s)= 2s+3/s(s2+5s+6)

3. Find the final values of the following (a) 1/s-2 (b) s-1/s(s+1) (c) X(s)=1/ s2+4

4. Find the inverse laplace transform of the function X(s)= 3 s2+ 8s+6/(s+2)(s2+2s+1)

5. Find the impulse response for the following circuit.





UNIT –VIII TUTORIAL SHEET NO:15

1 Find the Z-Transform and ROC of x(n)=an; a1

2 Find the Z-Transform of the signal x(n) =sinon u(n) and hence find ROC.

3 Determine the Z-Transform an ROC and locate its pole-zero of x(n)=(2/3 )nu(n)+ (-1/2)n u(n).

4 Determine the signal x(n) whose Z-Transform is given by X(z)= log (1-az-1); za.

5 Find x() when X(Z) = z+2/(z-0.8)2






UNIT –VIII

1. By using long division method determine inverse Z-Tranform of X(z)= 1+2z-1/1-2z-1+z-2

2. By using partial fraction method ,find inverssethe Z-transform. OfX(z)= ¼ z-1/(1-1/2z-1)(1-1/4z-1); 1/2.

3 By residue method solve X(Z)= z-1/(1-2z-1)( 1-3z-1) ROC 2 3

4. Solve the function in convolution method X(Z)= 1+3z-1/(1+3z-1+2z-2); 2

5. Find Inverse Z-Transform of X(z)= 8z-19/(z2-5z+6)


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