Harmonics Spikes

In this figure we can see the harmonics quite clearly they are shown as the vertical spikes which occm at even intervals. In addition to this, we can discern a spectral envelope, which is the pattern of amplitude of the harmonics. From om previous sections, we know that the position of the harmonics is dependent on the fundamental fi equency and the glottis, whereas the spectral envelope is controlled by the vocal tract and hence contains the information required for vowel and consonant identity. By various other techniques, it is possible to further separate the harmonics from the envelope, so that we can determine the fundamental frequency (useful for prosodic analysis) and envelope shape. 

Figures 12.4 and 12.5 show some typical power spectra for voiced and unvoiced speech. For the voiced sounds, we can clearly see the harmonics as the series of spikes. They are evenly spaced, and the fundamental frequency of the the source, the glottis, can be estimated by taking the reciprocal of the distance between the harmonics. In addition, the formants can clearly be seen as the more general peaks in the spectrum. The general shape of the spectrum ignoring the harmonics is often referred to as the envelope.

Figure 12.11 Steps involved in calculating the cepstrum. For demonstration purposes, an estimate of the spectral envelope has been overlaid on the two DFT spectra. The periodicity of the harmonics in the log spectram can clearly be seen, this gives rise to the spike at point 120 in the cepstrum. The low values (<30) in the cepstmm describe the envelope. It should be clear that these low values are separated from the spike - because of this it is a simple task to separate the source and filter.

Consider the magnitude spectrum of a periodic signal, such as that shown in Figure 12.11. As we have proved and seen in practice, this spectrum will contain harmonics at evenly spaced intervals. Because of the windowing effects, these harmonics will not be delta function spikes, but will be somewhat more rounded . For most signals, the amplitude of the harmonics tails off quite quickly... 

Again, as we would expect, because the periods were not sinusoidal, this has harmonics at multiples of the main spike. The amplitude effect will be present in the cepstrum also, but as this is varying much more slowly than the periods , it will be in the lower range of the cepstrum. As the amplitude effect is the spectral envelope and the spikes represent the harmonics (ie the pitch), we see that these operations have produced a representation of the original signal in which the two components lie at different positions. A simple filter can now separate them. 

In this figure we can see the harmonics quite clearly they are shown as the vertical spikes which occur at even intervals. In addition to this, we can discern a spectral... 

Figure 7.6 The log magnitude spectrum shows the pattern of harmonics as a series of evenly spaced spikes. The pattern of the amplitudes of the harmonics is called the spectral envelope, and an approximation of this is drawn on top of the spectrum.

Power Conditioner. A fuel cell produces DC power that must be converted to AC. The power conditioning section also reduces voltage spikes and harmonic distortions. 

The large oscillations starting at around 3.8 ms and 14 ms (Fig. 4-a) are attributed to the passage of two successive clouds of bubbles. The sudden variations (spikes) are the effect of external electrical noise. The amplitude of the second harmonic oscillation is 60 mV (estimated using a BPF, not shown here). 

Representative results are shown in Figure 12.3, with ATR spectra of the same polymers being shown for comparison [8], although it should be noted that the ATR spectra were measured at higher resolution than the photothermal spectra. The distortion of the stronger bands in the ATR spectra of the more polar polymers is caused by the effect of anomalous dispersion when an internal reflection element (IRE) with a relatively low refractive index, presumably ZnSe, was used. Remarkably the highest quality of photothermal spectrum was measured in the case of polypropylene, which has a relatively weak spectrum, and the lowest quality spectrum was measured in the case of Nylon 6, where the effect of photoacoustic saturation [10] is clearly evident. It is interesting to speculate on whether this spectrum and that of polycarbonate would have been improved had the velocity of the interferometer mirror been increased. Spikes in some of the spectra at 1082 and 1804 cm were attributed to supply frequency harmonics. 

Figure 11 Quasi-isothermal crystallization of polyamide 12 at 7 o=173°C, fp = 600s, ytr=0-5K. (a) Temperature profile consisting of an asymmetric sawtooth profile. The resulting heating rate and the heat flow rate show sharp spikes containing a broad spectrum of higher harmonics. (b) Specific reversing heat capacity as a function of time for different frequencies as indicated in the graph. The lines labeled Cp and Cp c indicate the data for liquid and crystalline polyamide 12 at 173 °C available from the ATHAS-DB, respectively. The used temperature time profile for sample preparation and crystallization is shown in the inset. Reproduced with permission from Schick, C. Anal. Bioanal. Chem. 2009, 395,1589-1611. ...

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