1.a. Differentiate between bilinear ZT and impulse invariant method.

1.b. Compute 4- point DFT of a casual four sample sequence given by X(n) = {j, 0, j, 1}

1.c. Explain the effect of quantization in computation of DFT.

1.d. Verify parseval's theorem for sequence $x(n)=\left(\frac{1}{2}\right)^{n} u(n)$. Assume N=4.

1.e. Differentiate between DSP processor and microprocessor.

2.a. Find DFT of the following sequence using DIT FFT algorithm.

X(n)={-1, -1, 2, 0, 2, 0, 2, 0} and sketch the magnitude and phase response.

2.b. Let x be a finite sequence with DFT

$ X=\operatorname{DFT}[x]=[0,1+j, 1,1-j] $

Using the properties of the DFT determine the DFT's of the following:

i) $y[n]=e^{j(\pi / 2) n} x(n)$

ii) $y[n]=\cos (\pi / 2) n \ x(n)$

iii) $y[n]=x[(n-1)_4]$

iv $y[n]=[0,0,1,0] \oplus x[n]$ with $\oplus$ denoting circular convolution

3.a. Design a Butterworth digital IIR low pass filter using Billinear transformation by taking T=0.5 second, to satisfy the following specification.

$\begin{aligned} 0.707 \leq &\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{jw}} | \leq 1.0 : 0 \leq \mathrm{w} \leq 0.45 \pi\right.\right.\\\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{jw}} | \leq 0.2\right.\right.& : 0.65 \pi \leq \mathrm{w} \leq \pi \end{aligned}$

3.b. Given that $\mathrm{H}(\mathrm{s})=\mathrm{s}^{3} /\left((\mathrm{s}+1)\left(\mathrm{s}^{2}+\mathrm{s}+1\right)\right)$ Find H(Z) using Billinear transformation method, for T=1.

4.a. Explain special features of TMS 320 c67XX DSP processor.

4.b. Consider the LTI system governed by the equation, y(n)+0.8301y(n-1)+0.7348y(n-2)= X(n-2) Discuss the effect of coefficient quantization on pole location when the coefficient are quantized by

(i) 3 bit of truncation and

(ii) 4 bits of truncation.

5.a. Design a linear phase FIR high pass filter using rectangular window by taking 7 window sequence and with cutoff frequency, $w_c=0.2 \pi$ rad/sample.

5.b.

6.a. Addressing modes of DSP processor? Where they are used.

6.b. Frequency transformation in digital domain.

6.c. DMA controller. Memory organisation of TMS320C6713