### Table 1: Mixing model and ICA solution

2006

"... In PAGE 1: ... 2) The use of all the information obtained from the basis vectors solves the permutation problem more accurately and therefore improves the BSS performance. Blind source separation in frequency domain Table1 shows equations related to a mixing model and ICA. Convolutive mixtures in the time domain can be approximated as multiple instantaneous mixtures in the frequency domain.... ..."

Cited by 2

### Table 1: The detection error rates of the time-domain source detection technique

"... In PAGE 3: ... The values were averaged over the neighboring 21 frames. The detection error rates are summarized in Table1 , where labeling a source as active when the source was inactive is defined as the false alarm rate, and labeling a source as inactive when the source was inactive is defined as the miss rate.... ..."

### Table 5. Computational complexity per symbol, time-domain filter length L, frequency- domain block length N.

2005

"... In PAGE 59: ... The time-domain equalizers are assumed to have length JL, which is the minimum lter length covering the receiver ISI window and consistent with the simulation con guration used for the results reported in the previous sections. An approximate operation count of the original recursive algorithm [36], the proposed square root recursion, the time-average approximation, the frequency-domain equalizer, and the frequency-domain matched lter approximation are tabulated in Table5 for a single equalization iteration. An approximate total op count as a function of the num- ber of separable channel multipaths for a 4 4 MIMO setup is also depicted in Fig.... ..."

### Table 1: Command file for time-domain fault simulation.

in SWITTEST: Automatic Switch-level Fault Simulation and Test Evaluation of Switched-Capacitor Systems

"... In PAGE 4: ... All simulations were performed on a SUN SPARC10 workstation. Time-domain fault simulation The SWITTEST command file of Table1 is used to drive a time- domain fault simulation for the differential filter of Figure 7. A 2 V differential signal at 100 KHz is considered at the filter input in the design specification.... In PAGE 5: ...05) in order to obtain some statistics on undetectable faults for this threshold value. Fault simulations have been carried out with both SWITCAP and HSPICE for a total of 144 faults given by the fault list of Table1 . Figure 8 shows the fault coverage given by SWITTEST as a function of test variable threshold.... ..."

### Table 2. BKYY DR for ICA and Blind Source Separation (BSS)

1997

Cited by 19

### Table 1: Operators corresponding to the coordinate axes of the chirplet transform parameter space Description 1-parameter Composite Time-domain notation notation g(t)

"... In PAGE 5: ... The parameters of these operations form an index into the chirplet family. The operations corresponding to the coordinate axes of the chirplet transform parameter space are presented in Table1 . The operators will be explained as they are used.... In PAGE 5: ... The operators will be explained as they are used. The general notion to keep in mind is that any combina- tion of these operators results in a 2-D a ne coordinate transformation in the TF plane, which may be represented using the homogeneous coordinates often used in computer graphics [35] ( Table1 , last column). The continuous STFT may be formulated as an inner product of the signal with the family of functions given in (2): Stc;fc = hgtc;fc;log( t)js(t)i (4) where t is a suitably-chosen ( xed) window size, and s(t) is the original signal.... In PAGE 5: ... We use the vertical bar between the arguments and absorb the conju- gation into the rst element so that we can write hgj by itself, as an operator that acts on whatever follows, in this case the signal, jsi. Suppose we take the Gaussian window, centered at t = 0, with unit pulse duration, as given by: g(t) = 1 pp exp(?12t2) (6) We denote a time shift to the position tc, with an oper- ator that has a multiplicative law of composition: ! ! tc ( Table1 ). A frequency shift to the position fc consists of multiplying the window by exp(j2 fct), which we will de- note quot; quot; fc.... In PAGE 5: ... A frequency shift to the position fc consists of multiplying the window by exp(j2 fct), which we will de- note quot; quot; fc. The single-operator notation ( Table1 , second column) consists of a pictorial icon depicting the e ect each operator has on the TF plane, even when the operator is acting in the time-domain. For example the symbol with the two up-arrows indicates a uniform upward shift along the frequency axis, of the time-frequency plane, for positive... In PAGE 6: ... Using the simpli ed law of compostion, we may com- pose a time shift by tc with a frequency shift by fc, as follows: ! ! tc quot; quot; fc = Ctc;0;0;0;0C0;fc;0;0;0 = Ctc;fc (8) where omissions from the parameter list of C indicate val- ues of zero. Equation 7) may be re-written, using the \Composite notation quot; ( Table1 , third column): Stc;fc = Ctc;fcg(t) s(t) (9) 2.3 Time-Frequency-Scale Volume The STFT is a mapping from a one-dimensional func- tion (the domain, which is a function of time) to a two- dimensional function (the range, which is a function of time and frequency).... In PAGE 7: ...5 Continuous Chirplet Transform (CCT) We have been using the frequency shear operator, which we obtained through multiplication by a linear FM chirp. In a dual manner, we may introduce the time shear operator ( Table1 , last row) which we obtain by convolving with a linear FM chirp. Fourier transformation of a chirp, with chirprate, d, produces another chirp which has chirprate ?1=d.... In PAGE 7: ... Again, the law of composition [38] of any two chirplet operators (multiplicatively) follows by virtue of the fact that both represent a ne coordinate transformations of the TF plane. The intuition behind (11) is that entries in the rst column of Table1 simply represent the coordinate axes of the multidimensional parameter space, and their subscripts represent the distances along these axes. Generalizations of the STFT and wavelet transform, that make use of chirping analyzing functions, have been previously suggested [28], [29], [39], [40], [41], [42], [43], [30].... In PAGE 8: ....6.4 Parallelogram-shaped tilings of the TF plane The method of multiple windows may be extended fur- ther to the chirplet framework. This further extension makes use of the same families of multiple windows that are used in the Thomson method, and that we rst extended to the true rectangular tiling of the TF plane, but instead they will now be used within the context of the operators of Table1 . In the same way that the Thomson method consists of computing power spectra with a plurality of windows, and averaging the power spec- tra together, we compute the power CCTs with a plurality of windows, and average the results together.... ..."

### Table 1: Operators corresponding to the coordinate axes of the chirplet transform parameter space Description 1-parameter Composite Time-domain notation notation g(t)

"... In PAGE 6: ... The parameters of these operations form an index into the chirplet family. The operations corresponding to the coordinate axes of the chirplet transform parameter space are presented in Table1 . The operators will be explained as they are used.... In PAGE 6: ... We use the vertical bar between the arguments and absorb the conju- gation into the rst element so that we can write hgj by itself, as an operator that acts on whatever follows, in this case the signal, jsi. Suppose we take the Gaussian window, centered at t = 0, with unit pulse duration, as given by: g(t) = 1 pp exp(?12t2) (6) We denote a time shift to the position tc, with an oper- ator that has a multiplicative law of composition: ! ! tc ( Table1 ). A frequency shift to the position fc consists of multiplying the window by exp(j2 fct), which we will de- note quot; quot; fc.... In PAGE 6: ... A frequency shift to the position fc consists of multiplying the window by exp(j2 fct), which we will de- note quot; quot; fc. The single-operator notation ( Table1 , second column) consists of a pictorial icon depicting the e ect each operator has on the TF plane, even when the operator is acting in the time-domain. For example the symbol with the two up-arrows indicates a uniform upward shift along the frequency axis, of the time-frequency plane, for positive values of the parameter.... In PAGE 6: ... Using the simpli ed law of compostion, we may com- pose a time shift by tc with a frequency shift by fc, as follows: ! ! tc quot; quot; fc = Ctc;0;0;0;0C0;fc;0;0;0 = Ctc;fc (8) where omissions from the parameter list of C indicate val- ues of zero. Equation 7) may be re-written, using the \Composite notation quot; ( Table1 , third column): Stc;fc = Ctc;fcg(t) s(t) (9) 5Segal [44] and others sometimes refer to these coor- dinate transformations as symplectomorphisms. It is well- known [12], [45] that the actual geometry of phase space is symplectic geometry, and that it is a coincidence that SP2 corresponds to area-preserving a ne geometry.... In PAGE 7: ...5 Continuous Chirplet Transform (CCT) We have been using the frequency shear operator, which we obtained through multiplication by a linear FM chirp. In a dual manner, we may introduce the time shear operator ( Table1 , last row) which we obtain by convolving with a linear FM chirp. Fourier transformation of a chirp, with chirprate, d, produces another chirp which has chirprate ?1=d.... In PAGE 7: ... Again, the law of composition [46] of any two chirplet operators (multiplicatively) follows by virtue of the fact that both represent a ne coordinate transformations of the TF plane. The intuition behind (11) is that entries in the rst column of Table1 simply represent the coordinate axes of the multidimensional parameter space, and their subscripts represent the distances along these axes. Segal exploited various coordinate transformations in the TF plane in the development of his theory of dynamical systems of in nitely many degrees of freedom [47].... In PAGE 9: ....6.4 Parallelogram-shaped tilings of the TF plane The method of multiple windows may be extended fur- ther to the chirplet framework. This further extension makes use of the same families of multiple windows that are used in the Thomson method, and that we rst extended to the true rectangular tiling of the TF plane, but instead they will now be used within the context of the operators of Table1 . In the same way that the Thomson method consists of computing power spectra with a plurality of windows, and averaging the power spec- tra together, we compute the power CCTs with a plurality of windows, and average the results together.... ..."

### Table 5 General terms ontologies in time domain

2004

"... In PAGE 7: ...able 4 Mapping records in smart space monitor............................................................. 41 Table5 General terms ontologies in time domain.... ..."

### Table 1: Performance of FF, RRT-Plan, and LPG on various domains. Entries list the number of problems the planner could not solve within ve minutes of CPU time. Domain FF RRT-Plan LPG

"... In PAGE 7: ... We generated 20 domains, starting with one block/goal atom and moving up to 20. Figure 5 shows the number of problems solved by the planners within a given time length, while Table1 shows the number of problems solved by FF and RRT-Plan on sev- eral standard planning domains. These statistics were gen- erated by allowing the planners to run for up to ve minutes and recording the time to completion.... In PAGE 7: ... RRT-Plan is of course a randomized algorithm and there- fore can produce different results on different runs. While we have not performed exhaustive testing, the numbers in Table1 change only slightly (in one test suite we observed only 6 failures on Pipesworld, in another 1 failure in Push- Block). This is probably because the average completion time for some problems is around the 5 minute cutoff and therefore variation can mean the problem sometime regis- ters as a failure.... ..."

### Table 1: Time domain HRV parameters

"... In PAGE 2: ... Fig 1. Average and SD of MeanNN HRV parameters Small differences were observed in time domain parameters before and after training (see Table1 ). At 6 months the HRV parameters show almost no difference.... ..."