7 Define Correlation of the sequence 8 State any two DFT properties 9 Why

7 define correlation of the sequence 8 state any two

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7. Define Correlation of the sequence. 8. State any two DFT properties. 9. Why impulse invariant transformation is not a one-to-one mapping? 1. a) Compute 4- point DFT of casual three sample sequence is given by, x(n) = 1/3, 0 _ n _ 2 = 0, else b) State and prove shifting property of DFT. 2. Derive and draw the radix -2 DIT algorithms for FFT of 8 points. 3. Compute the DFT for the sequence {1, 2, 0, 0, 0, 2, 1, 1}. Using radix -2 DIF FFT and radix -2 DIT- FFT algorithm. 4. Find the output y(n) of a filter whose impulse response is h(n) = {1, 1, 1} and input signal x(n) = {3, -1, 0, 1, 3, 2, 0, 1, 2, 1}. Using Overlap add overlap save method.
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5. In an LTI system the input x(n) = {1, 1, 1}and the impulse response h(n) = {- 1, -}Determine the response of LTI system by radix -2 DIT FFT 6. Find the output y(n) of a filter whose impulse response is h(n) = {1, 1, 1} and input signal x(n) = {3, -1, 0, 1, 3, 2, 0, 1, 2, 1}. Using Overlap save method UNIT IV: IIR DIGITAL FILTERS 1 . With a neat sketch explain the design of IIR filter using impulse invariant transformation. 2. Apply impulse invariant transformation to H(S) = (S +1) (S + 2) with T =1sec and find H(Z). 3. For a given specifications of the desired low pass filter is 0.707 _ |H(_)| _1.0, 0 _ _ _ 0.2_|H(_)| _ 0.08, 0.4 _ _ _ _ _ Design a Butterworth filter using bilinear transformation . 4. Explain the procedural steps the design of low pass digital Butterworth filter and list its properties . 5. The normalized transfer function of an analog filter is given by, 1H a (S n )= S n2 + 1.414S n +1 with a cutoff frequency of 0.4 _, using bilinear transformation . . 6. List the three well known methods of design technique for IIR filters and explain any one . 7. Design a low pass filter using rectangular window by taking 9 samples of w(n) and with a cutoff frequency of 1.2 radians/sec.Using frequency sampling method, design a band pass FIR filter with the following specification. Sampling frequency F s =8000 Hz, Cutoff frequency fc 1 =1000Hz, fc 2 =3000Hz.Determine the filter coefficients for N =7. 8. Design an ideal high pass filter with H d (e j _ ) = 1 ; _/4 _ | _| _ _= 0 ; | _| _ _/4 Using Hamming window with N =11
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9. Determine the coefficients of a linear phase FIR filter of length N =15 which has a symmetric unit sample response and a frequency response that satisfies the conditions H (2 _k /15) = 1; for k = 0, 1, 2, 3 = 0.4 ; for k = 4 = 0; for k = 5, 6, 7 10. Design and implement linear phase FIR filter of length N =15 which has following unit sample sequence H(k) = 1 ; for k = 0, 1, 2, 3 = 0 ; for k =4, 5, 6, 7 11. Convert the analog filter in to a digital filter whose system function is S + 0.2 H(s) = (S + 0.2) 2 + 9.Use Impulse Invariant Transformation .Assume T=1sec 12. The Analog Transfer function H(s)= ----------------.Determine H(Z) .Using Impulse (S+1) (S+2) Invariant Transformation .Assume T=1sec . 13. Apply Bilinear Transformation to H(s)= ------------- with T=0.1 sec. (S+2)(S+3) UNIT V: FIR DIGITAL FILTERS 1. Differentiate IIR filters and FIR filters. 2. Write the characteristics features of Hanning window 3. Define pre-warping effect? Why it is employed?
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