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.

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

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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- Spring '16
- DIGITAL SIGNAL PROCESSING
- Digital Signal Processing, sampling rate, Fir