Digital Signal Processing Reference
In-Depth Information
Clock (
f
s
)
Integrator
e
(
n
)
1
∼
x
(
t
)
Σ
x
(
t
)
y
(
n
)
LPF
−1
Quantizer
−1
Adaptive
x
(
n
)
z
−1
Δ
[ Adaptive DM Decoder ]
K
[.]
Δ
n
−1
z
−1
Δ
n
^
x
(
n
)
z
−1
[ Adaptive DM Encoder ]
Σ
Integrator,
Fig. D.18
Adaptive DM system
DSP Project
Part 1: Problem Solving Using MATLAB
(A) Prime numbers
(A-1) A prime number (p) is an integer that has no factors or divisors except 1
and itself. The first 12 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23,
29, 31, and 37. Note that 2 is the only even prime number. Prime
numbers play a significant role in coding and computation algorithms
and circuits.
(A-2) Write a MATLAB code to find whether a given integer x is a prime.
(A-3) Write a MATLAB code to find the number of primes less than or equal to
a given real number x (not necessarily an integer). This is called ''prime
counting function, p(x)''. For example, p(10) = p(10.9) = 4.
(A-4) Prime number theorem As x becomes large, p (x) approaches x
=
ln
ð
x
Þ
.
Prove using MATLAB simulation.
(B) Non-linear equations
Using MATLAB, find whether the equation cos(x) = x
2
has a solution over
the interval [ - 3, + 3].
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