An improved system and method for designing a mother wavelet. The system and method first displays on the screen a filter P(z), wherein a mother wavelet is associated with the filter P(z). The filter P(z) is a product of two low pass filters G.sub.0 (z) and H.sub.0 (z), which collectively comprise a perfect reconstruction filter bank which models the wavelet. The method then displays on the screen a plot which illustrates a zeros distribution of P(z), as well as other information, such as the mother wavelet function, correlations, frequency responses, etc. The user can then graphically adjust the zeros distribution of P(z) on the plot in order to obtain the desired mother wavelet. This involves factorizing P(z) into G.sub.0 (z) and H.sub.0 (z), wherein the factorizing includes assigning one or more of the zeros illustrated in the plot to the functions G.sub.0 (z) and H.sub.0 (z) in response to user input. The step of adjusting the zeros distribution of P(z) on the plot also includes selecting a type of filter P(z). The operation of adjusting the zeros distribution of P(z) operates to automatically adjust one or more of the mother wavelet, the correlation, and the frequency response which are displayed on the screen, thus providing immediate feedback as to the performance of the mother wavelet. This enables the user to make the optimum choice for the mother wavelet.
Interference from a spread-spectrum signal (e.g., GPS) is filtered out utilizing a wavelet-based method. A wavelet packet decomposition scheme generates a first plurality of coefficient sets from the signal(s). An entropy measurement is determined for each resulting wavelet decomposition level. Portions of the spread-spectrum signal occurring above the noise floor for the wavelet decomposition level having the lowest entropy measurement are then filtered out so that a revised coefficient set is generated therefor. As a result, a second plurality of coefficient sets can be formed such that the first plurality of coefficient sets differs from the second plurality of coefficient sets only by the revised coefficient set. A new signal is formed by applying a wavelet packet reconstruction scheme to the second plurality of coefficient sets.
The waveform signal analyzer of the present invention is equipped with: input means 10 that inputs a waveform signals; period detection means 20 that detects the period of the waveform signals inputted by input means 10; and division means 30 that divides the waveform signals by the period detected by period detection means 20. Wavelet transformation means 40 performs wavelet transformation of each individual division of the waveform signals. Display means 50 consecutively displays in time series the wavelet transformation results of each individual division of the waveform signals.
A wavelet generator for defining wavelets that represent a first signal includes a programmable filter bank, a frequency band controller coupled to the programmable filter bank, and a wavelet constructor coupled to the programmable filter bank. The programmable filter bank is operable to receive the first signal, and filter the first signal based upon a plurality of frequency bands to obtain a plurality of frequency band signals that each represent a frequency band of the first signal. The frequency band controller is also operable to receive the first signal. Moreover, the frequency band controller is further operable to obtain the plurality of frequency bands from the first signal, and program the programmable filter bank with the plurality of frequency bands. The wavelet constructor is operable to receive the plurality of frequency band signals.
A signal analyzer has a display with two regions. In a first region there is displayed a first waveform representing a signal. The first waveform is shown in two dimensions. One dimension represents signal amplitude and one dimension represents signal frequency. In a second region is displayed a second waveform. The second waveform represents a subset of data points of the first waveform. The second waveform also is shown in two dimensions. One dimension represents signal amplitude and one dimension represents signal frequency.
Systems and methods for urging a valve plug off a seat of a control valve and toward a set point in the absence of significant delay. Adjustable, user-selected input parameters to the input of a lead-lag filter in communication with the input of a control loop facilitates achieving tunable response by a control valve upon application of small amplitude inputs.
