Frequency-domain signal

Because they give access to the spectral representation of the signal, frequency-domain techniques are well suited for formant modification. The first step in frequency-domain formant modification techniques consists of obtaining a estimation of the spectral envelope. Based of the short-time representation of the signal, it. is possible to derive a spectral envelope function using a variety of different techniques. If the pitch of the signal is available, the short-time Fourier spectmm is searched for local maxima located around harmonic frequencies, then an envelope can be obtained by joining the local... 

In the work presented here, a slightly different two-parameter transient model has been used. Instead of specifying a center frequency b and the bandwidth parameter a of the amplitude function A(t) = 6 , a simple band pass signal with lower and upper cut off frequencies and fup was employed. This implicitly defined a center frequency / and amplitude function A t). An example of a transient prototype both in the time and frequency domain is found in Figure 1. 

Figure 1 Example of signal prototype in the time and frequency domains.

The results of both experiments showed that the analysis in the frequency domain provides new technological possibilities of testing characteristics of austenitic steels. Using known phase-frequency characteristics of structural noises it is possible to construct algorithms for separation of useful signal from the defect, even through amplitude values of noise and signal are close in value. 

Figure 9.45(b) shows fhe resulf of Fourier transformation (see Section 3.3.3.2) of the signal in Figure 9.45(a) from the time to the frequency domain. This transformation shows clearly that two vibrations, with frequencies of about 3.3 THz (= 3.3 x lo ... 

Bickel, H.J., and Rothschild, R.S., Real-Time Signal Processing in the Frequency Domain, Federal Scientific Monograph 3, March 1973. 

Spin-spin relaxation is the steady decay of transverse magnetisation (phase coherence of nuclear spins) produced by the NMR excitation where there is perfect homogeneity of the magnetic field. It is evident in the shape of the FID (/fee induction decay), as the exponential decay to zero of the transverse magnetisation produced in the pulsed NMR experiment. The Fourier transformation of the FID signal (time domain) gives the FT NMR spectrum (frequency domain, Fig. 1.7). 

FID Free induction decay, decay of the induction (transverse magnetisation) back to equilibrium (transverse magnetisation zero) due to spin-spin relaxation, following excitation of a nuclear spin by a radio frequency pulse, in a way which is free from the influence of the radiofrequency field this signal (time-domain) is Fourier-transformed to the FT NMR spectrum (frequency domain)... 

FT is essentially a mathematical treatment of harmonic signals that resolved the information gathered in the time domain into a representation of the measured material property in the frequency domain, as a spectrum of harmonic components. If the response of the material was strictly linear, then the torque signal would be a simple sinusoid and the torque spectrum reduced to a single peak at the applied frequency, for instance 1 Hz, in the case of the experiments displayed in the figure. A nonlinear response is thus characterized by a number of additional peaks at odd multiples of the... 

The evolution period tl is systematically incremented in a 2D-experiment and the signals are recorded in the form of a time domain data matrix S(tl,t2). Typically, this matrix in our experiments has the dimensions of 512 points in tl and 1024 in t2. The frequency domain spectrum F(o l, o 2) is derived from this data by successive Fourier transformation with respect to t2 and tl. 

Figure 1.22 Relationship of (a) the magnetization vector s position with (b) the signal time-domain NMR signal and (c) the frequency-domain NMR signal.

Apparently, the time-domain and frequency-domain signals are interlinked with one another, and the shape of the time-domain decaying exponential will determine the shape of the peaks obtained in the frequency domain after Fourier transformation. A decaying exponential will produce a Lorentzian line at zero frequency after Fourier transformation, while an exponentially decaying cosinusoid will yield a Lorentzian line that is offset from zero by an amount equal to the frequency of oscillation of the cosinusoid (Fig. 1.23). 

Fourier transformation of Rf pulses (which are in the time domain) produces frequency-domain components. If the pulse is long, then the Fourier components will appear over a narrow frequency range (Fig. 1.24) but if the pulse is narrow, the Fourier components will be spread over a wide range (Fig. 1.25). The time-domain signals and the corresponding frequency-domain partners constitute Fourier pairs. 

Figure 1.26 Free induction decay and corresponding frequency-domain signals after Fourier transformations, (a) Short-duration FIDs result in broader peaks in the frequency domain, (b) Long-duration FIDs yield sharp signals in the frequency domain.

In pulse NMR we measure in the time domain i.e., the variation of signal amplitude with time (FID) is recorded. These time-domain data are then subjected to Fourier transformation to convert them into the frequency domain. 

Single-quantum coherence is the type of magnedzadon that induces a voltage in a receiver coil (i.e., Rf signal) when oriented in the xy-plane. This signal is observable, since it can be amplified and Fourier-transformed into a frequency-domain signal. Zero- or multiple-quantum coherences do not obey the normal selection rules and do not... 

The spectral width SWj relates to the frequency domain. With the variation of the evolution period tj, the intensity and phase of the signals... 

There are actually two independent time periods involved, t and t. The time period ti after the application of the first pulse is incremented systematically, and separate FIDs are obtained at each value of t. The second time period, represents the detection period and it is kept constant. The first set of Fourier transformations (of rows) yields frequency-domain spectra, as in the ID experiment. When these frequency-domain spectra are stacked together (data transposition), a new data matrix, or pseudo-FID, is obtained, S(absorption-mode signals are modulated in amplitude as a function of t. It is therefore necessary to carry out second Fourier transformation to convert this pseudo FID to frequency domain spectra. The second set of Fourier transformations (across columns) on S (/j, F. produces a two-dimensional spectrum S F, F ). This represents a general procedure for obtaining 2D spectra. 

Once a smooth signal has been constructed, how is the trend represented Most of the available techniques do not provide a framework for the representation (and thus, interpretation) of trends, because their representations (in the frequency or time domains) do not include primitives that capture the salient features of a trend, such as continuity, discontinuity, linearity, extremity, singularity, and locality. In other words, most of the approaches used to represent process signals are in fact data compaction techniques, rather than trend representation approaches. Furthermore, whether an approach employs a frequency or a time-domain representation, it must make several major decisions before the data are compacted. For frequency-domain representations, assumptions about the... 

Transforms are important in signal processing. An important objective of signal processing is to improve the signal-to-noise ratio of a signal. This can be done in the time domain and in the frequency domain. Signals are composed of a deterministic part, which carries the chemical information and a stochastic or random part which is caused by deficiencies of the instmmentation, e.g. shot noise... 

---