(3)

i) Find the impulse response to get this response

ii) Find the size of the Hanning window to design a linear phase FIR filter with this

response (3)

b)Simplify the multirate system shown below and develop an expression for y(n) in terns of
x(n). (Use Vaidyanathan identities wherever applicable). Given H(z)= 2 <

(3)

H(z)

PART B

4. a) A decimator with M=3 is implemented with a FIR filter of length 12.
How can we reduce computational requirement using polyphase representation?
Compare thc computational requirements of direct implementation and polyphase
implementation. http:/ftvww.ktuonline.com (4)

b) A 4 channel analysis unifonn DFT filter bank has a set of filter transfer functions
18) k=0,1,2,3 ‏۔‎ HO(z) has polyphase compone
E,(z)=1+3z"'-0.82z7 8, (2)-2-1.52-3.12”
£(2)-4-0.9242.3” 85(2)-143.72"*1.72 components given as
i) Sketch the analysis section of the filter bank (2) ii) Determine Ho(z), Ht(z), H2(z), H3(z)

(3)

5. a) Discuss how STET overcome Heisenberg Uncertainity problem in time-frequency
analysis. Give illustrations of the windows used in finding Xr(K) (3)

1--7-1

b) Consider the filter response in one channel of analysis section HU(z)=2

i) Design a perfect reconstruction 2 channel QMF filter bank(2) ( Find HO),

ட Go(z),G,
ii) Sketch the complete analysis synthesis section (2) iii) Modify the above using

polyphase decomposition and noble identities to achieve computational simplicity

(2)

a) Find the wavelet coefficients W(a,b) for the signal f(t) as a function of b for different

values of a such that Use Haar wavelet

6.