Signal, band limited

In practice, since x(t) is a frequency band-limited signal, equation (11) shows that H(u) is known only on the finite interval wherein X(u) 0. There are also problems when the input signal is small, reduced to noise. 

Landau, 1960] Landau, H. (1960). On the recovery of band-limited signals after instantaneous companding and subsequent bandlimiting. BellSys. Tech. J., 39 351-364. 

Landau and Miranker, 1961] Landau, H. and Miranker, W. L. (1961). The recovery of distorted band-limited signals. J. Math. Anal.Appl., 2 97-104. 

Back propagation, 150 Band limited signal, 28 Bayes theorem, 127 Boxcar averaging, 36... 

Figure 9.7. Noise content of a fiberoptic oxygen sensor signal (a) in the time and (b) in the frequency domains. Time domain signals require broad frequency bandwidths. Frequency domain signals require very limited-frequency bandwidths. Noise is reduced by band limiting the signal, an advantage of frequency domain methods.

Typically, t(co) is small for co large. A spectrometer suppresses high frequencies. If the data i(x) have appreciable noise content at those frequencies, it is certain that the restored object will show the noise in a more-pronounced way. It is clearly not possible to restore frequencies beyond the band limit Q by this method when such a limit exists. (Optical spectrometers having sine or sine-squared response-function components do indeed band-limit the data.) Furthermore, where the frequencies are strongly suppressed, the signal-to-noise ratio is poor, and T(cu) will amplify mainly the noise, thus producing a noisy and unusable object estimate. 

Spectra-temporal weighting was found to be important only in quality judgements on speech codecs. Probably in music all spectra-temporal components in the signal, even silences, carry information, whereas for speech some spectra-temporal components, like formants, clearly carry more information then others, like silences. Because speech databases used in this paper are all telephone-band limited spectral weighting turned out to be only of minor importance and only the weighting over time had to be modelled. 

Spectral analysis techniques to study the behavior of pol3rmers subjected to dynamic mechanical loads and/or deformation is called Fourier Transform Mechanical Analysis (FTMA). FTMA measures the complex moduli over a range of frequencies in one test by exciting the sample by a random signal (band limited white noise) (13.14). FTMA overcomes or circumvents problems inherent in other test methods because it measures dynamic mechanical properties over a wide range of frequency with minimal temperature and moisture changes within the sample. 

A signal generator feeds band limited white noise into a power amplifier which drives an electro-mechanical shaker. A piezoelectric impedance head is mounted between the shaker and the... 

An alternative readout system is a scanning differential phase-contrast microscope with a split detector as shown in Figure 16.5. The optical configuration is compact and easy to align. The memory medium, in which the data bits have been recorded, is located at the focus of an objective lens. The band limit of the optical transfer function (OTF) is the same as that of a conventional microscope with incoherent illumination. The resolution, especially the axial resolution of the phase-contrast microscope, is similar to that obtained by Zemike s phase-contrast microscope. The contrast of the image is much improved compared to that of Zernike s phase-contrast microscope, however, because the nondiffracted components are completely eliminated by the subtraction of signals between two detectors. The readout system is therefore sensitive to small phase changes. 

As discussed previously with regard to sampling theory, real analytical signals are band-limited. The Fourier equations therefore should be modified for practical use as we cannot sample an infinite number of data points. With this practical constraint, the discrete forward complex transform is given by... 

Sigmoidal transfer function, 150 Signal averaging, 34 Signal, band limited, 27... 

A typical Raman spectrum of nanodiamond contains a number of signals that can be assigned to either sp - or sp -portions of the sample (Figure 5.16a). It apphes as a rule in doing so that all signals observed above 1360cm are related to the sp -portion as this value represents the band limit for sp -C-C-vibrations. 

For arbitrary, non-uniform sampling it is no longer possible to obtain a spectrum that is equal to a spectrum of continuous signal, even if it is strictly band-limited. Spectral artifacts, depending on the sampling schedule, appear as part of Point Spread Function. 

Fig. 9.7. Example of a Fourier transformation. The signal in time domain at left is the sine function, the magnitude of its Fourier transform is plotted at right. It is noted that F(co) is band limited.

According to Equation 52, the phase of the Fourier transformed signal in the frequency domain changes over the bandwidth of the instrument. This is, however, not the only phase problem that occurs. In addition, a frequency-dependent phase shift is introduced because the data collection can normally begin only a certain time (ca. 100 nsec) after the pulse is switched off. This and other phase shifts due to the use of band limiting filters are well-known in NMR and can easily be corrected with a digital computer. The true absorption spectrum, Sg(w), is obtained as a linear combination of the cosine and.sine Fourier transforms of the signal in the time domain Scos( ) SsinM respectively. 

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