Mathematical Morphology And Its Application On Signal Processing

It is normal to use the FFT method to analyze signals. This method is one kind of mathematical method that changes the time domain signals to frequency domain signal. Basically it transfers the original signals to the sinusoidal signals with different frequency. It selects the low-pass, high-pass, band-pass, band-stop filters to filter noise. It then reconstructs and restores the original signals. However, in reality, useful signals and noise in the frequency domain are inseparable, such as random noise, white noise.In order to solve this problem, Researchers have been searching for new methods. In recent years, image-based or visual signal characteristics of mathematical morphology have a broad application. The base idea of mathematical morphology is to use structure elements to detect an image to see whether the structure elements can be inserted into images. Such explicit descriptions of the geometric characteristics are more suitable for the processing and analysis of visual information.In images and signals processing fields, the powerful software is matlab. It's toolbox of FFT filter and wavelet filter that is effective. The researcher can apply correlative functions to analyze signals on the actual work. But a morphological toolbox has focused on two-dimensional image processing. The morphological toolbox does not provide the one dimensional signal processing function. Because mathematical methods have effective application on two-dimensional images processing, Programming software to process one-dimensional signals is rather valuable.This article is mainly about programming the software for processing one-dimensional signals. It is an in-depth study on the basic theory of mathematical morphology. It provide a one-dimensional morphological signal processing function, including erosion, dilation, opening, closing, opening-closing, closing-opening, and other operations. The above function s can be used to deal with signals contaminated by random noise. Structural elements in mathematical morphology is a very important concept, its shape, length obviously effect on the filtering results. In the latter the wavelet-filter and morphological filter were compared in processing sinusoidal signals and Doppler signals contaminated with random noise. The results indicated that the morphology method is superior to the wavelet method when processing single frequency in high frequent domain.