Digital Signal Processing Reference
In-Depth Information
1
0.5
0
−0.5
1
−1
0.8
0.6
0
10
20
30
(b) n (of W
n
)
0.4
1
0.2
0
0.5
−0.2
−0.4
0
−0.6
−0.5
−0.8
Unit Circle
−1
−1
0
10
20
30
−1
−0.5
0
0.5
1
(a) Real
(c) n (of W
n
)
Figure 3.12:
(a) Complex plane, showing the complex number having magnitude 0.9 and angle 45
degrees, i.e., 0.636 + j0.636; (b) Real part of complex power sequence; (c) Imaginary part of complex
power sequence.
• A script that allows you to dynamically see the impulse response and frequency response generated
by a pole or zero, or pair of either, as you move the cursor in the complex plane is
ML
_
DragPoleZero
3.6
CONVERSION FROM DECIMAL TO BINARY FORMAT
Digital systems represent all signals as sequences of numbers, and those numbers are expressed in binary
format using only two symbols, 1 and 0. Thus prior to discussing analog-to-digital conversion, it is
necessary to understand the basics of binary counting, since the output of an ADC is a binary number
that represents a quantized version of the analog input sample.
In our standard counting system, “Base 10,” the number 10 and its powers, such as 100, 1,000,
10,000, and so forth are used as the basis for all numerical operations.
For example, if you saw the decimal number “3,247” in print and read it out loud, you might say
“three thousand, two hundred and forty-seven, i.e., three thousand (or three times 10 to the third power),
plus another two hundred (two times 10 to the second power), plus another forty (four times 10 to the
first power), plus another seven (seven times 10 to the zero power).
