Noise aliasing

A second potential problem concerns aliased noise due to the increased spectral width. Digital filters, when combined with analog ones (Section 2-4c), do an excellent job of keeping unwanted noise (and signals, too ) from aliasing into the selected spectral window. This very efficient filtration can become a liability, however, if spectral widths are not carefully chosen, because the presence of signals that have been accidentally left outside of the spectral window is not revealed by the appearance of aliased resonances. 

Increasing the diameter, d, increases the number of photons in the wavefront measurement, and therefore reduces the error due to photon noise. However, increasing the diameter also increases aliasing in the wavefront sensor measurement. If the deformable mirror actuator spacing is matched to the subaperture size, then the fitting error will also depend on the subaperture diameter. There is therefore an optimum subaperture diameter which depends on the... 

Within the computational scheme described in the course of this work, the available information about the atomic substructure (core+valence) can be taken into account explicitly. In the simplest possible calculation, a fragment of atomic cores is used, and a MaxEnt distribution for valence electrons is computed by modulation of a uniform prior prejudice. As we have shown in the noise-free calculations on l-alanine described in Section 3.1.1, the method will yield a better representation of bonding and non-bonding valence charge concentration regions, but bias will still be present because of Fourier truncation ripples and aliasing errors ... 

The choice of sampling rate is sometimes governed by a tradeoff between frequency aliasing (low rate) and noise sensitivity (high rate). Quick and Bolgiano (1976) have employed the Poisson transformation to avert this complication. Consult Piovoso and Bolgiano (1970) for additional background on the Poisson transform. 

If there were no noise in the world, these factors would control the required sampling rate. However, because noise exists and noise can be aliased as well as data, the maximum noise frequency passed by the electronics system actually determines the required sampling rate. 

The truth of this is readily seen in the following hypothetical example. Assume that a spectrum of Gaussian lines is to be scanned at a rate such that the maximum Fourier component is 100 Hz. We might then establish the electronic bandpass such that a 100-Hz component is attenuated less than 3 dB. Without noise we would sample at 200 Hz. However, significant noise signals exist out to at least six times the passband frequency of 100 Hz, which means that we must sample at 1200 Hz to avoid aliasing the noise as we deconvolve. This is an extremely conservative approach, and one might well sample less frequently without difficulty. 

Under less restrictive noise/bandwidth considerations, one might drop the density to 6 points per resolution element at the risk of some minor noise aliasing. However, deconvolution by a factor of 3 would leave only two points per FWHM of a Gaussian spectrum-a number sufficient to characterize the spectrum, although display and measurement are difficult. 

Here vmax is the maximum wavenumber present (Nyquist wavenumber). Radiation v above vmax must be removed by suitable optical filtering or additional features and noise will be folded back onto the spectrum. Aliasing, as this phenomenon is called, places constraints on the operation of real... 

After the anti-aliasing filter, the analog/digital converter (ADC) quantizes the continuous input into discrete levels. ADC technology has shown considerable improvement in recent years due to the development of oversampling and noise-shaping converters. However, a look at the previous technologies [Blesser, 1978] [Blesser and Kates, 1978][Fielder, 1989] will help appreciate the current state-of-the-art. 

CDS is somewhat simpler since no demodulator and filter are needed. However, since the signal is sampled, CDS suffers from noise aliasing. Unless eliminated with appropriate circuit techniques [22, 23], this will result in an elevated noise floor. Chopper stabilization is preferred in printed circuit board implementations since all necessary components are readily available. 

Various circuits are used to simulate a large resistor with active components that take up significantly less chip area. A particularly simple solution consists of a switch that periodically charges the sense capacitors to a known value. This solution can be conveniently implemented in combination with correlated double sampling. Since the sensor capacitance is often small, the noise aliased by this resetting can be significant [22]. 

Fig. 4.2. Butyric acid MFC A loading images. Spatial patterns of activity identified at PC 1,4 and 10. Identification of noise and aliasing effects.

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