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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