## Discrete Time Signal Processing - Dec 18

### Electronics And Telecomm (Semester 5)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1. Solve any four**

**1.a.**State the relationship between DTFS, DTFT and DFT.

**1.b.**Differentiate FIR and IIR filters.

**1.c.**Differentiate fixed point and floating point implementations.

**1.d.**A digital filter has the following transfer functions. Identify type of filter and justify:

$\mathrm{H}(\mathrm{z})=\frac{\mathrm{z}}{\mathrm{z}+0.5}$

**1.e.**Explain how the speed is improved in calculating DFT by using FFT algorithm.

**2.a**A high pass filter is to be designed with following desired frequency response.

$\mathrm{H}_{\mathrm{d}}\left(\mathrm{e}^{\mathrm{jim}}\right)=0 \ -\frac{\pi}{4} \leq w \leq \frac{\pi}{4}$

$=\mathrm{e}^{-\mathrm{j} 2 \mathrm{w}} \ \frac{\pi}{4}\lt|w| \leq \pi$

Determine the filter coefficient h(n) if the window function function is defined as $\begin{aligned} w(n) &=1 \quad 0 \leq n \leq 4 \\ &=0 \quad \text { otherwise } \end{aligned}$

Also determine the frequency response $\mathrm{H}\left(\mathrm{e}^{\mathrm{jw}}\right)$ of the designed filter.

**2.b.**Compute circular convolution of following sequences using DITFFT and IDITFFT $\mathrm{x}_{1}(\mathrm{n})=\{1,2,1,2\}$ and $\mathrm{x}_{2}(\mathrm{n})=\{1,2,1\}$

**3.a.**Explain design steps for to design FIR filter using frequency sampling method.

**3.b.**Explain the mapping from S-plane to Z-plane using impulse invariance technique. Also explain the limitations of this method .

**4.a.**Design a Chebyshev-I filter with maximum passband attenuation of 2.5 dB at $\Omega \mathrm{p}=20$ rad/sec and stopband attenuation of 30 dB at $\Omega s=50 \mathrm{rad} / \mathrm{sec}$.

**4.b**Develop composite radix DIFFFT flow graph for N=6=3 x 2.

**5.a.**Design A Digital Butterworth filter that satisfies following constraints using bilinear transformation method . Assume Ts=1s

$0.707 \leq\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{jw}}\right)\right| \leq 1$ $0 \leq w \leq \frac{\pi}{2}$

$\left|\mathrm{H}\left(\mathrm{e}^{\mathrm{im}}\right)\right| \leq 0.2$ $\frac{3 \pi}{4} \leq w \leq \pi$

**5.b.**Explain the effects of finite word length in digital filters with examples.

**6.a.**Explain application of DSP processor in ECG signal analysis.

**6.b.**Draw neat architecture of TMS320C67XX DSP processor and explain each block.