M.Tech Degree I semester Examination in Electronics (Signal Processing)

SP 106-Multirate Signal Processing Model Question Paper

Maximum Marks: 50

Time: 3 hours

Module1

1. a) State and Prove the Noble Identities in Multirate Signal Processing. – 7 marks

b)Write short note on multistage systems in multirate signal processing. – 3 marks

OR

2. a) Show that the downsampling by M followed by upsampling by L and vice

versa are same only when L and M are mutually prime.

– 6 marks

b) Describe decimation and interpolation in multirate system. – 4 marks

Module2

3.a) Explain band pass sampling. Hence show that the anti-aliasing filter for decimation of

band pass signals is a complex band pass filter. – 5 marks

b) Describe Memory Saving Structures for FIR Poly-phase Decimators and Interpolators,

– 5 marks

OR

4. a) Show that the transpose of a factor of M decimator is a factor of M interpolator if the

transpose of a factor of M down sampler is a factor of M up sampler. – 5 marks

b) Let H(z) be a causal FIR transfer function of degree N-1 with N even,

H(z)= h[n]𝑧−𝑛𝑁−1

𝑛=0

Show that H(z) can be expressed in the form H(z) = (1+z-1

)H0(z2) + (1-z

-1)H1(z

2).

Express H0(z) andH1(z) in terms of the coefficients of the polyphase components E0(z)

and E1(z). – 5 marks

Module3

5. a) Design a polyphase realisation of the FIR filter employed for conversion of the

sampling rate from Fx=48 Khz to Fy= 32 Khz. – 7 marks

b) Describe computational efficiency of FIR interpolators and decimators – 3 marks

OR

6. a) Discuss the direct implementation structures for FIR decimators and interpolators.

– 5 marks

b) Consider the following IIR filter transfer function, H(z)=(1-2z-1

)/(1+3z-1

). Write down

expression for the type 1 polyphase implementation of the IIR filter with two polyphase

subfilter

– 5 marks

Module4

7. a) Show that the following FIR transfer function is a power symmetric function.

i) H0(z)= ½-z-1

+21/2 z-2

- 27/2 z-3

- 5z-4

- 5/2z-5

.

ii)H0(z) = 1+3z-1

+14z-2

+22z-3

-12z-4

+4z-5

. – 6 marks

b) Define i) Delay Complementary filter pairs

ii) Magnitude Complementary filter pairs

iii)All Pass Complementary filter pairs

iv)Power Complementary filter pairs – 4 marks

OR

8. a) Define Lth Band FIR Filters and discuss their properties. – 5 marks

b) Establish the relation between Nyquist filters and power complementary filters.

– 5 marks

Module5

9. a) What is Perfect reconstruction QMF filter banks? Give a 2 channel one and discuss.

– 6 marks

b) Consider a three channel filter bank with the synthesis filtersF0 (z) = 1, F1(z)= 2+ z-1

,

F2 (z)= 3+ 2z-1

+ z-2. Find a set of analysis filters such that the prefect reconstruction

property is satisfied. – 4 marks

OR

10.a) Write notes on

i) Uniform DFT analysis and synthesis filter banks

ii) Tree structured Multi-channel filter banks.

– 6 marks

b) Consider the two channel filter-bank below. Write down the analysis and synthesis filters.

Check whether the filter bank is PR.

– 4 marks

***