Noise-shaping filters

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. 

Temporal Noise Shaping (TNS). The TNS tool is used to control the temporal shape of the quantization noise within each window of the transform. This is done by applying a filtering process to parts of the spectral data. 

Subtractive synthesis uses a complex source wave—such as an impulse, a periodic train of impulses, or white noise—to excite a spectral-shaping filter. Linear prediction, or linear predictive coding (LPC), gives us a mathematical technique for automatically decomposing a sound into a source and a filter. For low order LPC (6-20 poles or so), the filter is fit to the coarse spectral... 

The frequency-shaping filter also modifies the spectrum of noise a further improved waveform differentiation can be achieved if it reduces the noise. A detailed analysis on noise is shown in Frequency-Shaping Filter and Spike Derivative . 

The effect of a frequency-shaping filter on noise can be quantitatively evaluated by the expression ... 

The quantitative impact of frequency-shaping filter on noise is affected by the recording system and biological environment, and the typical values of we observe vary around 2 within the signal band as shown in Fig. 18. Here, we use a = 2 to illustrate the analysis ... 

A reasonable beginning is that one needs about 24 dB of attenuation at the switehing frequency of the switching power supply. This, of course, should be modified in response to the actual conducted noise spectral shape. One determines the corner frequency of the filter by... 

Figure 9. Phase reconstruction of image reported in Figure 6 using the reference of image reported in Figure 8. The phase map is shown in (a), which includes a laterally averaged line-scan of 15 pixels, (b) A surface map of the two particles shape is displayed. The surface plot has been heavily noise filtered through Gaussian smoothing to better display the particles shape.

A practical limit to the sensitivity is also given by noise source external to the apparatus. Multistage mechanical filters are always used. We wish now to examine the possibility of realizing a gravitational antenna of the spherical shape. 

Several techniques have been proposed for modifying the shape of the short-time spectrum so as to emphasize those portions deemed to be important for speech perception or to reduce the amplitude of those portions assumed to be noise. One approach is adaptive comb filtering[Lim et al., 1978], In this method, the fundamental frequency of voiced speech sounds is estimated, and a comb fdter is then constructed to pass signal power in the regions of the pitch harmonics and to suppress power in the valleys in between. Experimental results with normal-hearing subjects, however, have shown no significant improvement in intelligibility with this type of system [Perlmutter et al., 1977][Lim et al., 1978],... 

There are several ways of detecting peaks in such noisy signals. The Wiener-Hopf filter minimizes the expectation value of the noise power spectrum and may be used to optimally smooth the original noisy profile [19]. An alternative approach described by Hindeleh and Johnson employs knowledge of the peak shape. It synthesizes a simulated diffraction profile from peaks of known width and shape, for all possible peak amplitudes and positions, and selects that combination of peaks that minimizes the mean square error between the synthesized and measured profiles [20], This procedure is illustrated... 

While the line-shapes parameters may not be unequivocally associated with a set of deterministic or theoretical parameters for a given system, the measurement model approach has been shown to adequately represent the impedance spectra obtained for a large variety of electrochemical systems. The line-shape models represent the low-frequency stationary components of the impedance spectra (in a Fourier sense). Regardless of their interpretation, the measurement model representation can be used to filter and thus identify the nonstationary (drift) and high-frequency (noise) components contained in the same impedance spectrum. 

First, either a Lorentzian or Gaussian filter is applied to the FID to reduce the amount of noise. The choice of lineshape will depend on the shape of the frequency domain spectrum, the lineshape is related to how the fluorine spins interact with their environment. The filter linewidth is generally similar to or slightly less than the T2 value (T2 can be estimated from the spectral linewidth). After application of the time domain filter, a fast Fourier transform (FFT) is performed. The resultant frequency domain spectrum will then need to undergo phase adjustment to obtain a pure absorption spectrum. The amount of receiver dead time (time lost between the end of the excitation pulse and the first useful detection time point) will determine the presence and extent of baseline artifact present as well as how difficult phase adjustment will be to accomplish. 

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