lay distortion (EDD). Mathematically, envelope delay is the derivative of the phase shift with respect to frequency. The maximum variation in envelope delay over a band of frequencies is called envelope delay distortion. Therefore, EDD is always a difference between the envelope delay at one frequency and that at another frequency of interest in the passband. It should be noted that envelope delay is often defined the same as group delay- - that is, the ratio change, with angular frequency, 5 of phase shift between two points in the network (Ref. 2). Figure 3.4 shows that absolute delay is minimum around 1700 and 1800 Hz in the voice channel. The figure also shows that around 1700 and 1800 Hz, envelope delay Frequency (kHz) Figure 3.4 Typical differential delay across a voice channel. 4 Wire-pair loading is discussed in Chapter 5. 5 Angular frequency and just the term frequency are conceptually the same for this text. Actually, angular frequency is measured in radians per second. There are 2 radians in 1 Hz. QUALITY OF SERVICE AND TELECOMMUNICATION IMPAIRMENTS distortion is flattest.6 It is for this reason that SO many data modems use 1700 or 1800 Hz for the characteristic tone frequency, which is modulated by the data. A data modem is a device that takes the raw electrical baseband data signal and makes it compatible for transmission over the voice channel. This brings up an important point. Phase distortion (or EDD) has little effect on speech communications over the telecommunications network. However, regarding data transmis- sion, phase distortion is the greatest bottleneck for data rate (i.e., the number of bits per second that a channel can support). It has probably more effect on limiting data rate than any other parameter (Refs. 3 and 4). 3.3.3 Noise 3.3.3.1 General. Noise, in its broadest definition, consists of any undesired signal in a communication circuit. The subject of noise and noise reduction is probably the most important single consideration in transmission engineering. It is the major limitin