Code No: NR210403

NR

Set No. 2

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II B.Tech I Semester Examinations,MAY 2011 SIGNALS AND SYSTEMS Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

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1. Assume a signal x ( t )= 6 cos 2π (5) t sampled at 7 Hz and 14 Hz. Illustrate the effect of sampling a signal at both frequency less than and greater than twice the highest frequency. Plot the output of the reconstruction filter. [12+4=16M]

2. (a) Prove the relationship between autocorrelation of a signal f(t) and its energy density spectrum. [8M]

or

(b) Determine and sketch auto correlation function of a periodic signal A Sin (wo t+θ). [8M]

3. (a) Define average power and obtain relationship between average power and power spectral density. [8M]

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(b) Derive the expression for Power Density Spectrum of a periodic signal. [8M] 4. (a) Write the significance of spectral analysis in communication systems.

[4M]

(b) Explain how a function can be approximated by a set of orthogonal functions. [6M] (c) Derive the expression by which the Mean square error can be evaluated. [6M] 5. (a) Find the inverse z transform of X (z) using power series method, given X (z)=1/[1-az−1 ],|z| < |a|. [8M]

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(b) Prove that for causal sequences the R.O.C in exterior of circle of some radius ‘r’. [8M]

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6. (a) Find the exponential fourier series and plot the magnitude and phase spectra of the following triangular wave form in figure 6a . [12M]

Figure 6a (b) State different properties of Fourier series.

1

[4M]

Code No: NR210403

NR

Set No. 2 [10M]

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7. (a) Find and sketch the convolution of two signals shown in figure4a:

Figure 4a (b) Find the Fourier transform of the following function: Cos ( 8t + 0.1π ) [6M]

or

8. (a) A Laplace transform is characterized by the differential equation d2 y(t) + 5 dy(t) +6y(t)=x(t), Solve for y(t) for t≥0 when x(t)=u(t), y(0− )=2 and dt2 dt dy(0−) = -12. [8M] dt (b) State and prove convolution and differentiation properties of Laplace transform. [4+4=8M]

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2

Code No: NR210403

NR

Set No. 4

in

II B.Tech I Semester Examinations,MAY 2011 SIGNALS AND SYSTEMS Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

ld .

1. Assume a signal x ( t )= 6 cos 2π (5) t sampled at 7 Hz and 14 Hz. Illustrate the effect of sampling a signal at both frequency less than and greater than twice the highest frequency. Plot the output of the reconstruction filter. [12+4=16M] 2. (a) Find the inverse z transform of X (z) using power series method, given [8M] X (z)=1/[1-az−1 ],|z| < |a|.

or

(b) Prove that for causal sequences the R.O.C in exterior of circle of some radius ‘r’. [8M] [10M]

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3. (a) Find and sketch the convolution of two signals shown in figure4a:

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Figure 4a (b) Find the Fourier transform of the following function: Cos ( 8t + 0.1π ) [6M]

Aj

4. (a) A Laplace transform is characterized by the differential equation d2 y(t) + 5 dy(t) +6y(t)=x(t), Solve for y(t) for t≥0 when x(t)=u(t), y(0− )=2 and dt2 dt dy(0−) = -12. [8M] dt (b) State and prove convolution and differentiation properties of Laplace transform. [4+4=8M]

5. (a) Find the exponential fourier series and plot the magnitude and phase spectra of the following triangular wave form in figure 5a. [12M]

3

NR

Set No. 4

Figure 5a (b) State different properties of Fourier series.

in

Code No: NR210403

[4M]

6. (a) Define average power and obtain relationship between average power and power spectral density. [8M]

ld .

(b) Derive the expression for Power Density Spectrum of a periodic signal. [8M]

7. (a) Prove the relationship between autocorrelation of a signal f(t) and its energy density spectrum. [8M]

or

(b) Determine and sketch auto correlation function of a periodic signal A Sin (wo t+θ). [8M] 8. (a) Write the significance of spectral analysis in communication systems.

[4M]

(b) Explain how a function can be approximated by a set of orthogonal functions. [6M]

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(c) Derive the expression by which the Mean square error can be evaluated. [6M]

Aj

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4

Code No: NR210403

NR

Set No. 1

in

II B.Tech I Semester Examinations,MAY 2011 SIGNALS AND SYSTEMS Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

ld .

1. Assume a signal x ( t )= 6 cos 2π (5) t sampled at 7 Hz and 14 Hz. Illustrate the effect of sampling a signal at both frequency less than and greater than twice the highest frequency. Plot the output of the reconstruction filter. [12+4=16M] 2. (a) Define average power and obtain relationship between average power and power spectral density. [8M]

or

(b) Derive the expression for Power Density Spectrum of a periodic signal. [8M]

[10M]

uW

3. (a) Find and sketch the convolution of two signals shown in figure4a:

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Figure 4a (b) Find the Fourier transform of the following function: Cos ( 8t + 0.1π ) [6M]

Aj

4. (a) Find the exponential fourier series and plot the magnitude and phase spectra of the following triangular wave form in figure 4a. [12M]

Figure 4a (b) State different properties of Fourier series.

[4M]

5. (a) Find the inverse z transform of X (z) using power series method, given X (z)=1/[1-az−1 ],|z| < |a|. [8M]

5

Code No: NR210403

NR

Set No. 1

(b) Prove that for causal sequences the R.O.C in exterior of circle of some radius ‘r’. [8M] 6. (a) Prove the relationship between autocorrelation of a signal f(t) and its energy density spectrum. [8M]

in

(b) Determine and sketch auto correlation function of a periodic signal A Sin (wo t+θ). [8M] 7. (a) A Laplace transform is characterized by the differential equation d2 y(t) + 5 dy(t) +6y(t)=x(t), Solve for y(t) for t≥0 when x(t)=u(t), y(0− )=2 and dt2 dt dy(0−) = -12. [8M] dt

ld .

(b) State and prove convolution and differentiation properties of Laplace transform. [4+4=8M] 8. (a) Write the significance of spectral analysis in communication systems.

[4M]

or

(b) Explain how a function can be approximated by a set of orthogonal functions. [6M] (c) Derive the expression by which the Mean square error can be evaluated. [6M]

Aj

nt

uW

?????

6

Code No: NR210403

NR

Set No. 3

in

II B.Tech I Semester Examinations,MAY 2011 SIGNALS AND SYSTEMS Common to Electronics And Telematics, Electronics And Control Engineering, Electronics And Instrumentation Engineering, Electronics And Communication Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

ld .

1. (a) Find the inverse z transform of X (z) using power series method, given X (z)=1/[1-az−1 ],|z| < |a|. [8M]

(b) Prove that for causal sequences the R.O.C in exterior of circle of some radius ‘r’. [8M] 2. (a) Write the significance of spectral analysis in communication systems.

[4M]

or

(b) Explain how a function can be approximated by a set of orthogonal functions. [6M] (c) Derive the expression by which the Mean square error can be evaluated. [6M]

uW

3. (a) Define average power and obtain relationship between average power and power spectral density. [8M] (b) Derive the expression for Power Density Spectrum of a periodic signal. [8M] [10M]

Aj

nt

4. (a) Find and sketch the convolution of two signals shown in figure4a:

Figure 4a (b) Find the Fourier transform of the following function: Cos ( 8t + 0.1π ) [6M]

5. (a) Prove the relationship between autocorrelation of a signal f(t) and its energy density spectrum. [8M] (b) Determine and sketch auto correlation function of a periodic signal A Sin (wo t+θ). [8M] 6. (a) Find the exponential fourier series and plot the magnitude and phase spectra of the following triangular wave form in figure 6a. [12M] 7

NR

Set No. 3

Figure 6a (b) State different properties of Fourier series.

in

Code No: NR210403

[4M]

ld .

7. Assume a signal x ( t )= 6 cos 2π (5) t sampled at 7 Hz and 14 Hz. Illustrate the effect of sampling a signal at both frequency less than and greater than twice the highest frequency. Plot the output of the reconstruction filter. [12+4=16M]

8. (a) A Laplace transform is characterized by the differential equation d2 y(t) +6y(t)=x(t), Solve for y(t) for t≥0 when x(t)=u(t), y(0− )=2 and + 5 dy(t) dt2 dt dy(0−) = -12. [8M] dt

or

(b) State and prove convolution and differentiation properties of Laplace transform. [4+4=8M]

Aj

nt

uW

?????

8

NR Set No. 2

Figure 4a. (b) State different properties of Fourier series. [4M]. 5. (a) Find the inverse z transform of X (z) using power series method, given. X (z)=1/[1-az−1],|z| ...
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