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Questions from the topic - 4. Discrete filter structures [8 hours] - Digital Signal Analysis and Processing
  1. Draw lattice structure for given pole-zero system $$ H(z) = (0.5 + 2z^{-1} + 0.6z^{-2})/(1-0.3z^{-1} + 0.4z^{-2}) $$. - 2070 Ashad
  2. What do you mean by Limit Cycle? How it occurs in recursive system? - 2070 Ashad
  3. What is the condition satisfied by Linear Phase FIR filter? Show that the filter with h(n) = {-1, 0, 1} is a linear phase filter. - 2070 Ashad
  4. Determine the Direct Form II realization of the following system.
    y(n) = -0.1y(n-1) + 0.72y(n-2) + 0.7x(n) - 0.252x(n-2). - 2069 Chaitra
  5. Compute the lattice coefficients and draw lattice structure of the following FIR system. $$ H(z) = 1 + 2z^{-1} - 3z^{-2} + 4z^{-3} $$. - 2069 Chaitra
  6. Realize the system function $$ H(z) = \frac{\left(1-\frac{1}{3}z^{-1}\right)\left(1-\frac{1}{4}z^{-1}\right)\left(1-\frac{1}{8}z^{-1}\right)}{\left(1-\frac{5}{6}z^{-1}\right)\left(1-\frac{1}{6}z^{-1}\right)\left(1-\frac{3}{4}e^{-j\frac{\pi}{4}}z^{-1}\right)\left(1-\frac{3}{4}e^{j\frac{\pi}{4}}z^{-1}\right)} $$ in terms of cascade of second order sections. Draw the block diagram of the cascade realization. - 2067 Mangsir
  7. Show by giving examples that the quantization error by truncation for sign magnitude number, $ e_{tsm}, $ lies in the range $ -(2^{-b} - 2^{-b_{u}}) \leq e_{tsm} \leq (2^{-b} - 2^{-b_{u}}) $ and that for the 2's complement number, $ e_{t2c}, $ lies in the range $ -(2^{-b} - 2^{-b_{u}}) \leq e_{t2c} \leq 0. \space b_{u} $ is the number of bits before quantization and b is the number of bits after quantization. - 2067 Mangsir
  8. How does an IIR filter differ from an FIR filter? - 2067 Mangsir
  9. Realize the overall system function: $$ H(z) = \frac{(1-\frac{1}{5}e^{-j\frac{\pi}{5}}z^{-1})(1-\frac{1}{3}z^{-1})(1-\frac{1}{5}e^{j\frac{\pi}{5}}z^{-1})}{(1-\frac{4}{5}z^{-1})(1-\frac{1}{7}e^{j\frac{\pi}{7}}z^{-1})(1-\frac{1}{5}z^{-1})(1-\frac{1}{7}e^{-j\frac{\pi}{7}}z^{-1})} $$ In terms of direct form I and direct form II structures. Draw the corresponding block diagrams of direct form I and direct form II structures. - 2068 Bhadra
  10. Differentiate between direct form I and II with suitable block diagrams. - 2065 Baisakh
  11. Compute and draw the lattice structure of given FIR filter. $$ H(z) = 2 + 0.35z^{-1} + 0.3z^{-2} + 0.45z^{-3} + 0.55z^{-4}. $$ - 2065 Baisakh
  12. Define one's complement, 2's complement and sign magnitude representation of numbers. Represent 80/136 in 8 bit 1's complement form. - 2065 Baisakh
  13. Compute and draw the lattice structure of given FIR filter. $$ H(z) = 1 + 0.4z^{-1} + 0.6z^{-2} + 0.25z^{-3} + 0.35z^{-4} $$ - 2065 Baisakh-Old
  14. Define One's complement, 2's complement and sign magnitude representation of numbers. Represent 192/220 in a 8 bit 2's complement form. - 2065 Baisakh-Old