In this thesis, visualization of complex domain in signal transform is studied. The theory and method of pseudo-color encoding display for vector expressing is proposed. Corresponding encoding displays of complex domain for a variety of signal transform types are implemented. The holo-spectrogram encoding display for wavelets transform of speech signal is studied emphatically, and some primary features of wavelets holo-spectrogram are analyzed. Analysis of complex transform domain is important method for signal processing. A complete complex domain should include a real field and an imaginary field, and is usually represented as magnitude spectrogram and phase spectrogram. Traditional signal analysis emphasizes on magnitude or power spectrogram only. Since 1980's. researches on signal feature of phase information and on reconstruction from phase have been more and more emphasized. Phase spectrogram of signal complex transform is difficult to be represented so far. due to the limitation on display method and technique. Usually, two-dimensional phase spectrogram can be expressed only as a plane picture with grayness-modulation, even as a half tone picture. The expression of obtained phase spectrogram is discontinuous and difficult to read out exactly. Moreover, the representation on traditional phase spectrogram is isolated from its magnitude spectrogram, and the inherent relation between phase and magnitude in the complex transform domain can not be reflected. The theory and method of holo-spectrogram encoding display is proposed and studied in this thesis, which can represent the magnitude and phase spectrograms of complex transform domain overall and simultaneously. The complex vectors are processed and encoded in the holo-spectrogram encoding display, according to their magnitude modules and phase angles. For a two-dimensional complex transform domain in time-frequency (or space-frequencies), a synthesized display in four-dimension, i.e. in time-frequency-magnitude-phase, can be obtained with the holo-spectrogram encoding display. Optimization and selection of the pseudo-color encoding domain for holo-spectrogram display is studied in the thesis. The surface of the twin-cone with white and black apexes in the Color space is chosen as the basic pseudo-color encoding domain. The magnitude components are presented with the brightness, while the phase components with the color hue. Therefore, it keeps the consistency in variation of grayness with traditional spectrogram, and guarantees the continuity of phase display, due to the continuity and reticulation of chromatic variation in the color space. Several concrete methods and ranges of pseudo-color encoding can be chosen for different applications. The resolutions of color hue and brightness are optimized. The pseudo-color encoding displays with high or finite resolution are proposed and implemented, respectively. Moreover, the pseudo-color encoding display
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