### Table 1.1, we summarize the desirable properties of the transforms and the coe cient processing techniques for many signal processing tasks. We emphasize that the desired property of wavelets can often be measured point- wise on the wavelet transform coe cients, so the measures are often additive. This motivates us to construct abstract algorithms that can minimize any additive measure, then use an appropriate measure for the problem at hand. In this sense, we construct a general framework for wavelet based applications. Simple adjustments result in a powerful algorithm for any particular task. The construction and analysis of the general framework is the ultimate goal of this thesis. Task Desirable transform Coe cients processing

### Table 2: New Signal constructs and extensions .

"... In PAGE 9: ...Irina Smarandache, Paul Le Guernic (| H := sample{ max(0, - apos;), n }(I) | K := sample{ max(0, apos;), d }(I) clk affinef n, apos;,d g( X,Y ) , | H ^= X) (n; d gt; 0 and apos; 2 6Z) | K ^= Y |) / H, K, I Finally, Y := unsamplef n, apos; g( X, Z), with n gt; 0 and apos; 2 6Z, de nes Y as an a ne oversampling using X and Z: (| clk_affine{ n, apos;, 1 }(X, Y) Y := unsamplef n, apos; g( X, Z) , | Y := ( X when ^Y ) default Z (n gt; 0 and apos; 2 6Z) | Y ^= Z |) Table2 summarizes the a ne processes and their associated clock equations. For an arbitrary clock H, we note [H]( apos;;n) the clock obtained by down-sampling with phase apos; and period n on H and (H)(n; apos;;d) the result of an a ne transformation of parameters (n; apos;; d) applied to the clock H.... ..."

### Table 4 Analysis and synthesis filters with PR property corresponding to semi-orthogonal wavelets estimated from different signals

2004

"... In PAGE 11: ... Case 2: Again, the proposed method is applied on two clips: one music clip and the other a speech clip. The analysis/synthesis filters designed from the signal itself based on this theory are tabulated in Table4 . The semi-orthogonal infinitely/com- pactly supported matched wavelet and corre- sponding scaling clips in Fig.... ..."

### Table 4: Mean Square Error (MSE) and computation time for coding and reconstruc- tion of piano and speech signals with compression corresponding to D = 3 for various sizes of data frame. Coifman 12 wavelets were used.

1997

"... In PAGE 26: ... It is thus to be expected that better matches between domain and range blocks, and correspondingly lower error values, should be obtained. Table4 indicates the mean square errors and computation times associated... ..."

Cited by 3

### Table 1 Comparison of signal feature extraction among HHT, wavelet, and fourier spectral analyses.

2003

"... In PAGE 7: ...provide additional information even in cases when the structural behavior is nonlinear and non-stationary. Table1 highlights some of the differences of these methods. An alternative approach for structural health monitoring that does not use modal properties is to represent the dynamic response of a structure in terms of the superposition of traveling waves that can traverse individual elements of a struc- ture, reflecting off boundaries to establish stand- ing waves from constructive interferences.... ..."

Cited by 3

### Table 1: Characteristics of speech codecs commonly used in packet networks.

"... In PAGE 3: ... Waveform codecs directly or indirectly code the amplitude of the signal, while CELP codecs are based on a model of the acoustics of the vocal tract during speech production. Table1 provides a summary of the codecs that are commonly used. The delay caused by the codec of choice needs to be minimized.... ..."

### Table 1. Hopfield Neural Network Applications

"... In PAGE 4: ... The applications of HNN include image [25] and speech processing, control, signal processing, database retrieval, fault-tolerant computing, pattern classification and recognition [20], automatic target recognition [24], olfactory processing, knowledge processing, while for the analog version we have applications such as image and signal processing, control, olfactory processing, pattern recognition [24], and in combinatorial optimization [12] problems. Many applications of the HNN in industry are described in ( Table1 ) [18]. In [23], the application of HNN in automatic target recognition is reviewed.... ..."

### Table 1 Primitive constructs in the Signal language Name Syntax Interpretation Semantics

"... In PAGE 6: ...3 Signal Semantics We are now ready to express the semantics of the Signal language and its tagged model as a transition system. A Signal process is the conjunction of a set of basic Signal statements, listed Table1 along with their interpretation semantics. Each variable v in the Signal speci cation is represented by two variables in the transition system: (1) variable v for holding the data, ranging over the same domain as in the speci cation, and (2) variable v for the clock, ranging over a binary domain to indicate presence or absence of a value in v.... In PAGE 6: ... In a run, we denote the k-th value in the sequence by vk and the k-th clock by v k. The statements in Table1 are divided into three categories. Monochronous (\single-clocked quot;) equations require all input and output signals to be present at the same time.... In PAGE 8: ... From the root, these two nodes are on di erent branches { meaning that both clocks will never be present at the same time. Now, let us describe the Signal statements in Table1 for clock relations. The statement for clock extraction, Z:=^X, is used to specify that signal Z describes the clock of X.... In PAGE 9: ... We de ne each stuttering run s = s0; ?; ?; ?; ?; s1; ?; :::; ?; s2; ::: to be equivalent to the run = s0; s1; s2; ::: obtained from s by removing all stut- tering (?) states. We now describe how each equation of Table1 can be translated to a... In PAGE 10: ... The corresponding automaton has two states: one for ring the reaction and one where the reaction is in a stuttering state. The equations in Table1 ensure that the ring state can be entered only when all clocks are present, and that the stuttering state can be entered only when all clocks are absent. These constraints express the assumption that, for arithmetic operations, the only allowable behaviors for the environment are the monochronous behaviors, with respect to signals X, Y and Z.... ..."

### Table 1: Facial animation parameters (FAPs) that are estimated from the speech signal. animation parameters we use a simple three layer feed-forward neural network trained by backpro- pagation. Because of the low computational com- plexity of such a network, we can determine the parameters from the speech signal in real-time. The audio signal is preprocessed leading to ele- ven input parameters for the network. First, the speech signal s(t) is divided into non-overlapping blocks of length T=33.33 ms corresponding to a frame rate of 30 Hz. The energy of the signal in each block i of length M

1997

"... In PAGE 4: ... These parameters are derived di- rectly from an audio signal of a speaking person. Five such parameters ( Table1 ) that are related to mouth and lip movements are used. Other facial expressions like eye blinking or global head mo- vements can be added to increase the realism of the animation.... ..."

Cited by 9

### Table 2: Objective speech quality versus signal-to-noise ratio for original degraded speech (100 8 kHz sampled TIMIT sentences with additive noise), enhanced speech processed with Auto-LSP and the proposed Noise Adaptive Auto-LSP algorithm.

in An Improved (Auto:I,LSP:T) Constrained Iterative Speech Enhancement for Colored Noise Environments

"... In PAGE 7: ... C. Evaluation Results Results of the algorithm evaluations are summarized in Table2 . Here, the Itakura-Saito Likeli- hood measure for the original degraded speech, enhanced speech processed using traditional Auto- LSP, and enhanced speech processed using the proposed Noise Adaptive Auto-LSP algorithm is shown.... ..."