Sine artifacts

Another problem with all the dwell time methods is that sinee a speeifie diameter tool is often used to do the polishing, the finished surfaee has a "roughness" of a spatial frequency associated with the tool diameter. This rather eo-herent roughness ean produce diffraction artifacts in the image produeed by the telescope. A partial solution to this problem is to use several tool sizes and do the figuring in stages rather than all at onee. 

The sine-bell functions are attractive because, having only one adjustable parameter, they are simple to use. Moreover, they go to zero at the end of the time domain, which is important when zero-filling to avoid artifacts. Generally, the sine-bell squared and the pseudoecho window functions are the most suitable for eliminating dispersive tails in COSY spectra. 

Fig. 15 Apodization, or the reduction of artifacts in the spectral line by the multiplication of the interferogram by a window function that tapers to zero at the end point of the interferogram. (a) Cosine interferogram of Fig. 13(a) multiplied by the triangular window function of Fig. 14(d). (b) Resulting spectral line, the sine-squared function.

Figure 8.7 Digital Sine function - the frequency response for a zero order hold interpolator sample rate converter with L = 4, which puts the original Nyquist frequency at 0.25 7t. We can see rolloff in the passband of about -3.9 dB and very poor rejection of images outside of the passband, which result in artifacts perceived as pitch shifting distortion.

Another perspective of looping is to consider the waveform as a sum of sinusoids. Each sinusoid at the loop start must have the same amplitude and phase as the sinusoid at the loop end in order to avoid splice artifact. If any component sinusoid does not line up in amplitude and phase, then there will be a click at the frequency of the sinusoid. The click should have the spectrum of a Sine function translated to the frequency of the sinusoid that does not line up. 

As described in the Section 3.3, two supposedly identical detectors are arranged to sample the signal simultaneously along x and y. However, the two detectors are usually not quite identical, and the reference signals to the detectors may not differ by precisely 90°. Also, the sample-and-hold circuits that follow the detectors may have slightly different characteristics. Three types of artifacts result (1) a DC offset between quadrature channels, (2) a gain difference between channels, and (3) a phase difference between channels. In terms of Eq. 3.5, artifact (1) means that there are constant terms of different magnitude added to the sine and cosine terms, while (2) and (3) imply different values of C and 4 rf respectively, for the sine and cosine terms. 

Lithic artifacts were collected from three sites south of the industrial town of Sines along the western coast of the southern Portuguese Alentejo province (see Map I). Two of these sites, Samouqueira and Palheiroes do Alegra, are 30 km apart on cliffs above the modem sea shore the third site, Fiais, is 12... 

A similar approach was presented by Keeler in application to heteronuclear J spectra with highly truncated echo modulation [87]. Truncation of signal, used for sensitivity reasons, results in sine wiggles . These artifacts can be suppressed by apodization, although at the expense of resolution. Keeler showed that CLEAN is an inexpensive alternative to the maximum entropy method, which can also remove truncation artifacts without degrading resolution. 

Fig. 4 shows the highly distorted TMS artifact at C5 and FC5 which are nearby the TMS coil. The TMS artifact at C5 shows the distorted waveform relative to the damped sine wave at Cz. The TMS artifact at FC5 implies that it contains the higher order components in the residual component. 

In contrast, truncation at a computationally feasible (i.e., small) value of R. produces artifacts when the system is strongly ionic because the potential energy is dominated by the slowly varying 1/r terms.To address this, a popular approach known as Ewald or lattice sum (similar to the one used to calculate the lattice energy of ionic crystals) is used to sum the electrostatic interactions in the simulation box and all of its replicas. This is done by rewriting the sum of the 1/r terms as a sum of a rapidly converged series in real space (so a small cutoff can be used for these terms) and a much more slowly varying smooth function that can be approximated by a few cosine and sine terms in reciprocal (k) space.These are expensive calculations that scale like... 

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