Sound waveforms

For musical sounds, it is common to store Just a loop, or table, of the periodic component of a recorded sound waveform and play that loop back repeatedly. 

The acoustic vibrations of musical sound do not in general have a sine waveform because various musical instruments are involved and higher harmonics of the fundamental tone are included, and hence the instantaneous frequency is defined as half the number of zero-crossing of the sound waveform per second. 

C. Method for Measuring the Laser-Induced Sound Waveform... 

Frequency analysis of the induced-sound waveform of pork shown in Fig. 2 was performed between 0 and 15 ms. Fig. 6 shows the result. The frequency with the highest amplitude was 40 kHz. Fig. 7 shows the frequency characteristics of the samples shown in Fig. 3. 

Fig. 2 Laser-induced sound waveform by CW CO2 laser. The induced sound has an intermittent waveform. The laser-induced sound generated at a time of 0 ms is termed the first laser-induced sound...

The laser-induced sound waveform was characterized by (a) the pressure amplitude, (b) the attenuation time, (c) the ratio of the first and third peaks, (d) the fall time (third peak) (see Fig. 4). These parameters are defined as follows. The pressure amplitude is defined as the difference between the maximum and minimum pressures of the laser-induced sound. The attenuation time is defined as the time that the laser-induced sound pressure decreases from it maximum value to 1/lOth its maximum value. The ratio of the first to third peaks is defined as the ratio of the first peak height to the third peak height. The fall time is defined as the time for the pressure to change from 0 to its value at the third induced sound peak. 

Fig. 3 First laser-induced sound waveforms of various tissues. The samples exhibit different sound amplitudes and waveforms...

Fig. 4 Analysis of laser-induced sound waveforms (1) pressure amplitude, (2) attenuation time, (3) ratio of the first and third peaks, (4) fall time...

An intermittent laser-induced sound waveform was generated by various samples. The laser-induced sound waveform varied depending on the kind of tissue. This... 

A note of caution should be sounded here. Whilst the curves shown in Figure 6.5 are characteristic of many charged dispersions it should be recalled that once we apply a sinusoid to a non-linear system the response need not be a sinusoid. As the strain is increased into the nonlinear region, the waveform passing through the sample becomes progressively distorted. The instrumental analysis in this case involves... 

Research into the acoustics of musical instruments has revealed considerable evidence that aperiodicity and noise play an important role in the sound quality of a musical instrument. This research reinforces the justifications for using more than one period for looping in sampling. Since the loop is actually a periodic waveform, the number of samples in that loop of course determines the number of spectral components that can be present in the spectrum, and their frequency spacing. N samples are completely specified by N/2 complex Fourier components. At 44100 Hz sample rate, for a 256 sample loop, the spacing between frequencies would be 44100/256 = 172 Hz. Noise or other aperiodic components would be forced to fall on one of these bins. The longer the loop, the closer that spectral components can become, and the more aperiodic they can become. A truly aperiodic waveform would need an infinite loop, but our perception mechanism can be fooled into perceiving aperiodicity with a much shorter loop. 

Even more interesting sounds can be made by more complex usage of the FM formulas. With frequency modulation one might select more than one modulating waveform, or perhaps different waveforms than sinusoids. In addition, a complex amplitude modulation can be imposed. For example, one possibility is revealed in the trigonometric relation... 

Its waveform retains the random quality of the original signal, and likewise the excitation signal in the gap matches the surrounding excitation. Hence the sub-optimal interpolant is likely to sound more convincing to the listener than the LSAR reconstruction. 

In this section it is shown that a large class of acoustical waveforms including speech, music, biological, and mechanical impact sounds can be represented in terms of estimated amplitudes, frequencies and phases of a sum of time-varying sine waves. There are many signal processing problems for which such a representation is useful, includ-... 

Any sound can be visualized as a waveform, like the cross section of a ripple on a pond. When in the 64 mode, the Commodore 128 is capable of reproducing four different waveforms. Three of them (the triangle, sawtooth, and pulse waves) produce clear tones, and the fourth (the noise wave) makes a rushing or hissing sound. Figure 1 represents each of these waveforms. You can assign any one of the four waveforms to any of the 128 s three sound channels, or voices. 

As you ll discover by experimenting, these special effects work well with certain combinations, and poorly (or not at all) with others. Ring modulation works only when you set the carrier voice to the triangle waveform. Synchronization works with any waveform, but synchronizing any frequency with the noise waveform (a nearly random combination of many frequencies) doesn t accomplish much. The sawtooth and pulse waves often sound similar. 

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