1.a. Compare Impulse invariant method and BLT method

1.b. If $x[n]=\{1,2,1,2\},$ determine $X[K]$ using DIF FFT

1.c. State and prove frequency shifting property of DFT.

1.d. Write a short note on replication.

1.e. State advantages of digital filters.

2.a. Develop composite radix DITFFT flow graph for $N=6=2 \times 3$

2.b. Design a digital Butterworth filter that satisfies following constraints using bilinear transformation method. Assume $\mathrm{T} \mathrm{s}=0.1 \mathrm{s}$ .

$0.8 \leq\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{i} \mathrm{w}}\right)\right| \leq 1 \quad 0 \leq \mathrm{w} \leq 0.2 \pi$ $\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{i} \mathrm{w}}\right)\right| \leq 0.2 \quad 0.6 \pi \leq \mathrm{w} \leq \pi$

3.a. Explain Dual Tone Multifrequency Detection using Goertzel’s algorithm.

3.b. Design a linear phase FIR low Pass filter of length 7 and cut off frequency 1 rad/sec using Hamming window.

4.a. Compute DFT of $x[n]=\{1,2,3,4,5,6,7,8\}$ using DITFFT algorithm.

4.b. Explain Finite word length effects in digital filters.

5.a. Explain Architecture of TMS320C67XX DSP processor with the help of neat block Diagram

5.b. Find DFT of $x(n)=\{1,2,3,4\} .$ Using these results and not otherwise find DFT

i) $x_{1}(n)=\{4,1,2,3\}$

ii) $x_{2}(n)=\{2,3,4,1\}$

iii) $x_{3}(n)=\{6,4,6,4\}$

6.a. Obtain digital filter transfer function by applying impulse invariance transfer function.

$\mathrm{H}(\mathrm{s})=\frac{\mathrm{s}}{(\mathrm{s}+5)(\mathrm{s}+2)}$ if $\mathrm{Ts}=0.1 \mathrm{s}$

6.b. Explain application of DSP processor to radar signal processing

6.c. Write short note on limit cycle oscillations