**EE6403 Discrete Time Systems and Signal Processing Important Questions**

**Unit 1**

1.For each of the following systems, determine whether the system is static stable, causal, linear and time invariant a) y(n) = x(n) where x(n) [x(n+1) — x(n)] b) y(n) = x(n) x(n-1) c) y(n) = ax(n) +b d) y(n) = n x(power)2 (n) e) x(n) cos wOn .

2. Give the classification of signals and explain it. Give the various representation of the given discrete time signal x(n) = {-1,2,1,-2,3} in Graphical, Tabular, Sequence, Functional arid Shifted functional.

3. Explain the significance of Nyquist rate and aliasing during the sampling of continuous time signals

4. Explain the different types of mathematical operations that can be performed on a discrete time signal.

5. Classify and explain different types of signals with examples. (10 marks)

6. State the properties of DTS. Determine if the system described by the following input-output equations are linear or non-linear. i) y(n) = x(n) + (x(n-1)) ii) y(n) = x2 (n) iii) y(n) = nx(n)

7. 'Write short notes'about the' applications, merits and demerits of DSP

**Unit II**

1. State and prove convolution property cif-discrete time fourier transform. Determine the convolution sum of two sequences x(n) = {3,2,1,2}, h(n) = (1,2,1,2)

2. Solve the difference equation y(n) -3y(n-1) — 4y(n-2) = 0,n>= 0 ,y(-1) = 5 9. Compute the response of the system y(n) = 0.7 y(n-1)-0.1.2y(n-2) +x(n-1)+x (n-2)to the input x(n) = n u(n).

3. Determine the system function and impulse response of the system described by the difference equation y(n) = x(n) +2x(n-1)- 4x(n-2) + x(n-3)

4. Determine the z- transform and ROC of the signal x (n) = [3(2n )- 4 (3n )] u(n). 16. State and prove convolution theorem in z-transform.

5. State and prove the following properties of z-transform.1) Time shifting ii) Time reversal iii) Differentiation iv) Scaling in z-domain.

6. Given x(n) = 6(n) + 2 6(n-1) and y(n) =3 6(n+1) + 6(n)- 6(n-1). Find x(n) * y(n) and X(z) Y(z)

7. Find the convolution of the signals x(n) = 1 n = -2,0,1 = 2 n = -1= 0 elsewhere h(n) = 6(n)- (n-1)+ 6(n-2)- 6(n-3)

**Unit III**

1. Explain any five properties of DFT.

2. Explain the decimation in frequency radix-2 FFT algorithm for evaluating N-point DFT of the given sequence. Draw the signal flow graph for N=8.

3. Compute the 8-point DFT of the sequence x(n) = 1, 0 <= n <= 7 0, otherwise by using DIT,DIF algorithms.

4. What are the differences and similarities between DIT and DIF FFT algorithms?

5. An 8-point discrete time sequence is given by x(n) = [2,2,2,2,1,1,1,1]. Compute the 8-point DFT of x (n) using radix-2 FFT algorithm.

6. Find the circular convolution of x(n) = 1,2,3,4) and h(n) ={413,2,1} (8 marks)

7. Derive DIF — FFT algorithm. Draw its basic butterfly structure and compute the DFT x(n) = (-1)n using radix 2 algorithm.

**Unit IV**

1. Explain the design of FIR filters using windows.

2. Using a rectangular window technique design a Iowpass filter with pass band gain of unity, cutoff frequency of 1000 Hz and working at a sampling frequency of 5 kHz. The length of the impulse response should be 7.

3. Draw the structure for IIR filter in direct form — I and II for the following transfer Function H (z) = (2 + 3 11) (4+ 2 z-1 +3 12) / (1+0.6 11) (1+ 1' +0.5 z-z)

4. Design a Butterworth (or) a Chebyshevanalog high pass filter that will pass all radian frequencies greater than 200 rad/sec with no more that 2 dB attuenuation and have a stopband attenuation of greater than 20 dB for all less than 100 rad/sec

**Unit V**

1. Explain the functional modes present in DSP processor

2. Explain about MAC unit and pipelining in DSP.

3. Explain the function of auxiliary registers in the indirect addressing mode to point the power

4. Write short notes on auxiliary registers, memory mapped register addressing, circular addressing mode.

5. Explain the architecture of TM5320050 with a neat diagram.

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