**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 log_{2} and log_{10}, 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 ...

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