Footnotes

Chapter 14

1 The MATLAB help files refer to D N as the “Dirichlet function,” but in nearly all of the mathematical literature, D N (or minor variants thereof) is called the “Dirichlet kernel.” The term “Dirichlet function” is usually reserved for the function defined as

Chapter 16

1 For the figures in this note, the DTFT results and the DFT results are each plotted against a different abscissa, as explained in Math Box 16.1.

Chapter 23

1 Equivalent noise bandwidth is also called noise equivalent bandwidth or simply noise bandwidth. The subscript “neq” is used here because “eqn” is so often used as an abbreviation for “equation.”

Chapter 60

1 Because the concept of analyticity is different for continuous-time and discrete-time signals, some authors distinguish the discrete-time case by using special notation or terminology. In [1], Marple initially uses the term analytic-like, and then transitions to using quotation marks around “analytic.”

2 The usual convention for denoting the Hilbert transform is a script uppercase H, despite the fact that this notation can be easily confused with the italic uppercase H typically used to denote the transfer function of a filter.

3 In discussing the figure, it is convenient to borrow some terminology from the A/D converter community. In discussions of A/D converters, the frequency band from 0 to f_s/2 is called the first Nyquist zone. The band from f_s/2 to f_s is called the second Nyquist zone, and so on. However, negative frequencies are not considered. We can extend the terminology by calling the band from 0 to f_s/2 the first positive Nyquist zone and calling the band from 0 to – f_s/2 the first negative Nyquist zone.