State the time reversal property of DFT with an example.

(b) Compute the eight-point DFT of the sequence using the radix-2 decimation-in-time algorithm.

2.(a) With a neat diagram, show the computation of 8-point DFT using radix-2 DIF algorithm. Draw the realisation of an LTI system with input and output that satisfies the difference equation
y[n

3. Discuss Goertzel algorithm and state its application.

4. What are linear phase filters ?State the conditions in which an FIR filter can be a linear phase filter.

5. Design an FIR low pass filter satisfying the specifications <img src='./qimages/8811-5.jpg'>

By applying a Kaiser window to the impulse response for the ideal discrete low pass filter with cut-off wc 0·64n.

6. Design a Butterworth filter using bilinear transformation method for the following specifications <img src='./qimages/8811-6.jpg'>

7. Determine the first 15 coefficients of FIR filters of the magnitude specification given below using frequency sampling method:

<br><br> <img src='./qimages/8811-7.jpg'>

8. Draw the realization by using direct form-II implementation of the LTI system with system function
<img src='./qimages/8811-8.jpg'>

9. Consider an FIR lattice filter with coefficients k1 k3 Determine the FIR filter coefficients for the direct form structure.

10.(a) Summarize the difference between overlap-save method and overlap-add method
State and prove the circular convolution property of DFT.