THE SPECTRAL VIEW
Certainly the history of a signal is of fundamental importance, but a substantially deeper appreciation of the composition of the signal isprovided by “spectral analysis”. The spectral views of the signals discussed earlier also are presented in the right-hand panels of Figures 3.1 to 3.5. (Only The magnitude spectra are shown in these figures; discussed later.) A signal´s spectrum also provides another basis by which we can categorize the basic types of signals. The spectrum derives, again, from the Fournier transform of the timehistory, wherein the signal’s function is discomposed into components of amplitude and phase across frequency. A spectrum may be discrete or continuous. The word continuous is used in the context of both time and frequency domains (i.e., apropos temporal and spectral views, respectively), but the word has rather different meaning in to each view. Periodic signals that are ongoing or steady state,whether simple or complex, are continuous in time and are uniquely characterized by discrete spectra. Here too the simplest example is the sinusoid or pure tone (Fig. 3.1 A), the graph of the spectrum that is a point whose coordinate is a single amplitude ( and phase, not shown) at its singular frequency. Rather than plot a single point, a line is dropped from the point to the abscissa- thefrequency axis / Fig. 3.1. right). Consequently, discrete spectra are known as line spectra. More complex periodic signals ( e.g., Figs.3.1,B and C, and 3.2, A and B) demonstrated spectra showing more lines, following naturally from the fact that they are composed of two or more ( perhaps even an infinite number of) discrete tones. The
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Spectra illustrated here are idealized; real - world analysis suffers from practical exigencies. Both stimulus generation and analysis requires windowing of the functions involved, hence creating transients. Still, with appropriate methods and choice of parameters, the ideal is well approximated, ever for the quasi – periodic complex tone of the steady – state portion ofa vowel sound. (See Fig. 3.6 B, right; the nearly line like components in the graph of the spectrum start and are spaced at the fundamental frequency of the voice, related or the nearly constant periods of repetition in the temporal view.)
In constraint, both transients and random noise (i.e., a periodic signals) ten to be characterized by continuous spectra ( e.g., Figs. 3.3 to 3.5). The notionof continuous in frequency means that the energy in the signal is distributed across frequency rather than focused at discrete frequencies, even if uneven un amplitude across frequency. Thus, the tone burst´s spectrum ( Fig. 3.4) has its and downs in amplitude but characteristically demonstrates a central band like concentration – the main lobe – with two or more smaller lobes above and below thecarrier frequency, called side lobes (also, especially in radio communication, side bands). Again, the distribution of energy is continuous, or seamless, whiting the main lobe and side lobes, even if to latter are many. Sal analysis permits a particularly instructive comparison between the DC pulse (as used to generate the acoustic click) and tone bursts. The a of the latter are quite the pulse´sspectrum, and for good reason. While no longer packaged as neatly as the energy reminiscent of those of the of continuous tones, the energy of sinusoidal pulses is still concentrated around the nominal frequency of the carrier, and the spread of energy above and below follows patterns imposed by the spectrum of the gating or windowing function itself. in figure 3.4, this again is a simple...