Digital Communication Systems

Glossary

Conventions and Notations

1.  The symbol | | means the absolute value or magnitude of the complex quantity contained within.

2.  The symbol arg( ) means the phase angle of the complex quantity contained within the brackets.

3.  The symbol Re[ ] means the “real part of” and Im[ ] means the “imaginary part of” the complex quantity contained within the brackets.

4.  The natural logarithm is denoted by ln.

5.  Logarithms to bases 2 and 10 are denoted by log₂ and log₁₀, respectively.

6. The use of an asterisk as superscript denotes complex conjugate; e.g., x* is the complex conjugate of x.

7.  The symbol ⇌ indicates a Fourier-transform pair, e.g., g(t) ⇌ G(ƒ), where a lowercase letter denotes the time function and a corresponding uppercase letter denotes the frequency function.

8.  The symbol F[ ] indicates the Fourier-transform operation on a time function enclosed within the brackets, e.g., F[g(t)] = G(ƒ).

The symbol F^–1[ ] indicates the inverse Fourier-transform operation of a frequency function enclosed within the brackets, e.g., F^–1[G(f)] = g(t).

9. The symbol ★ denotes convolution, e.g.,

10.  In Chapter 10 on error-control coding, the symbol ⊕ is used in the figures, but when it comes to binary arithmetic, the modulo-2 addition is denoted by an ordinary plus sign throughout that chapter; the same statement applies to Appendix J on maximal-length codes.

11.  The use ...