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DSP Final Examination
PART-I. Conceptual Problems: (50%)
(Close Book)
1-1.
Explain the following four terminologies: (20%)
(a) Decimation in Frequency FFT (8-point);
(b) Row-Column 2D FFT Method;
(c) General Discrete Transform;
(d) FIR Filter Design by Windowing.
1-2.
There are eight FIR filters, whose impulse responses (starting from
n
= 0) are
h
1
(
n
) : [3, 1, 2, 1, 3];
h
2
(
n
) : [3, 1, 2, 2, 1];
h
3
(
n
) : [3, 1, 2, 1, 2];
h
4
(
n
) : [4, 2, -1, -1,
2,
4];
h
5
(
n
) : [4, 2, -3,
3, -2, -4];
h
6
(
n
) : [4, 2, -3,
5, -3,
2];
h
7
(
n
) : [4, 2, -3, -5,
3, -2];
h
8
(
n
) : [1, 3, 2, -4, 6, 2].
Please give your decision reasons first and identify which filters are
(a) Linear phase filter (7%)
(b)
H
i
[
k
] (the DFT of
h
i
[
n
]) is real for all
k
(8%)
1-3.
Explain the following three convolutions (10%)
(a) Linear Convolution;
(b) Periodic Convolution;
(c) Circular Convolution;
For what condition (what kind of data), these three convolutions will be the same. (5%)
PART II.
DFT Properties and Computation (60%)
2-1.
An
8-point
sequence is given as
x
8
[
n
] = [3
4 -2
7 -4
1 -5
2], its DFT is expressed by
X
8
[
k
]. By
16-point
DFT program, we can compute
X
16
[
k
] = DFT
16
(
x
[
n
]), where we pad 8 extra zeros in the end). Please

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