1.Describe the concept of frequency in continuous time and discrete time sinusoidal signals

Ans: Waveforms and Derivation

2.State and prove sampling theorem .

Ans: Statement, Derivation, Reconstrution

3.Explain the classification of DT signals.

Ans: a.Linear and non linear systems.

b.Static and dynamic system

c.Causal and noncausal system

d.Stable and unstable system.

4.State and prove the properties of Z transform.

Ans: 1.Linearity

2.Time shifting

3.Convolution

4.Time reversal

5. Differentiation in Z domain

6. Correlation

7.Multiplication

8.Parseval’s theorem

9.Initial Value theorem

10.Final value theorem

5.Problems on Z transform and inverse Z transform.

6.State and prove the properties of DFT.

Ans: 1.Linearity

2. Time reversal

3.Circular convolution

4.Circular symmetries

5. Symmetry properties

6. Circular correlation

7.Priodicity

8.Parseval’s theorem

7.Explain the methods of filtering long data sequences.

Ans: Overlap add method

Overlap save method

Diagrams

8.Derive 8 point radix –2 DIT-FFT algorithm.

Ans: Basic butterfly diagram, Derivation, Complete butterfly diagram.

9. Derive 8 point radix –2 DIF-FFT algorithm

Ans: Basic butterfly diagram, Derivation, Complete butterfly diagram.

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10. Derive 16 point radix –4 DIF-FFT algorithm.

Ans: Basic butterfly diagram, Derivation, Complete butterfly diagram.

11.Draw the structures of IIR filters

Ans: Direct form I

Direct form II

Cascade structure

Parallel structure

Lattice Ladder structure.

12.Derive the equation for designing IIR filter using backward difference method.

Ans: maping from S plane to Z plane.

d/dt y(t)=y(nT)-y(nT-T)/T

13. Derive the equation for designing IIR filter using impulse invariant method.

Ans: Maping from S plane to Z plane.

Impulse invariant equation

14. Derive the equation for designing IIR filter using bilinear transformation.

Ans: maping from S plane to Z plane.

Bilinear equation S=2/T(1-Z-1/1+Z-1)

15.Problems IIR filter design

16.Explain the steps involved in the design of FIR filter using window technique.

Ans: Specify the equation of window function

Find h(n)

Find hd(n)=h(n)w(n)

Find H(ω)

17. Explain the steps involved in the design of FIR filter using frequency sampling technique.

Ans: Find G(k) from given Hr(k)

Find H(k)

18. Explain the steps involved in the design of FIR filter using Kaiser window .

Ans: Determine hd(n)

Choose δ

Calculate α

Determine the parameter α s

Choose the parameter

Find N

Calculate yhe window function wk(n)

Find h(n)=wk(n) hd(n)

19. Draw the structures of FIR filters.

Ans: Direct form

Cascade structure

Parallel structure

Lattice structure.

20.Problems on design techniques and structures of FIR filters.

21.Explain the different types of representations in digital systems.

Ans:Fixed Point

Floating point

Block floating point

22.Disscuss the different types of quantization errors.

Ans:Input quatization error

Proct quantization error.

Coeffient quantization error

23.Derive the expressions for quatization noise power.

Ans: Input quantization noise power

output quantization noise power

24.Explain the different types of limit cycle oscillations and also the solutions

Ans: Zero input limit cycle oscillations

Overflow input limit cycle oscillations

Solutipn:scaling

25.Explain the construction and operation of channel vocoder with block diagram.

Ans : Block diagram

Explanation.