Clipping operations

It is sometimes necessary to extract information about the fundamental period (and thus also the fundamental frequency) or about the period of the longest component (lowest frequency) in a complex signal. The fundamental period (frequency) is the longest period (lowest frequency) in a spectrum of harmonically related tones. In a given signal with non-harmonically related components, it may not necessarily be the lowest frequency. Two simple measures are available for this purpose:

1. distance between peaks of the same sign (i.e. positive or negative),
2. the distance between zero-crossings of the same sense (i.e. positive-going or negative-going).

The measures may be combined. The measures are valid for sinusoid signals. However, sometimes it is necessary to extract the fundamental period (and thereby also the fundamental frequency) of a complex signal. For complex signals, however, the method will not work in the general case, because the ripples which are due to harmonics or other higher frequency components may have a peak amplitude which is comparable with that of the fundamental frequency (or, more generally, with the lowest frequency), or they may cause additional zero crossings, as shown in the Figures.

The time-domain operations used as a heuristic measure to reduce the effects of higher amplitude harmonics are the clipping operations:

1. Peak clipping. A maximum amplitude level whose absolute value is lower than the expected amplitude of spurious peaks is defined. Positive and negative instantaneous amplitude values of the signal are limited to the corresponding positive and negative signed values.
2. Centre clipping. A minimum amplitude level whose absolute value is higher than the expected amplitude of peaks associated with spurious zero-crossings is defined. Positive and negative instantaneous amplitude values of the signal are limited to the corresponding positive and negative signed values.

The two operations may of course be combined; applications of these operations are shown in the Figures. The operations are in fact quite widely used to pre-process the signal for fundamental frequency analysis. The operations are also used in simple forms of `signal compression' in narrow-band radio transmission, to increase the total energy (at the expense of distortion) in the transmitted signal; more sophisticated compression techniques are used in practice, however.

  
Figure 14: Complex signal with non-fundamental peaks and zero crossings.

  
Figure 15: Peak clipped signal.

  
Figure 16: Centre clipped signal.

  
Figure 17: Peak and centre clipped signal.