11-05-2012, 01:37 PM
Phase Spectra Analysis for Signal Recognition and Sequencing Applications
phase spectral anlyses using fourier series.pdf (Size: 398.31 KB / Downloads: 36)
Phase Spectrum for Imaging Information Analysis
This paper is aimed at developing phase spectrum methods and technology to analyze information for recognition static and dynamic images produced by serially organized data. These include voice, sound, serial business data, etc.
Phase Spectrum Background
Spectrum analysis plays a central role in the area of voice recognition and similar applications dealing with time dependent series. It takes in the time series and subjects it to a Fourier transform, either in its analytical form or in computer digitized form, using the Fast Fourier Transform (FFT).
FFT discover information that could define sound’s harmonics, their power spectra used in voice and other sources of sound analysis and recognition technology. Similarly, power spectra found applications in chemistry to discover chemical components, in earth science, communications, electronics, etc., [1] - [5].
Phase Spectrum Technology
Phase spectrum is the other by-product of the FFT. It provides the relative position of the source data's components, their harmonics' phases as a function of frequency.
Phase spectrum requires additional transformation into a readable and applicable characterization of the original information.
This paper will address research of the phase spectrum methodology, phase spectrum attributes, and its measurable characterization.
This paper presents phase spectra derived from FFT of various serial data that provides basis for development and application of phase spectrum technology, and discuss phase technology applications to various sequencing data, such as voice, sound, and image recognition.
The phase spectrum for this serial data displays tense concentration at the sidebands and fast alternating divergence at the center frequencies.
In contrast, the phase spectrum of the second set of serial data displays only moderate concentration at the side bands, and moderate variation at all other frequencies.
Phase Spectrum of Serial Data
depicts a result of a FFT transform of data containing the information of a noised, single note sound of a musical instrument. MathLab software was used to perform the FFT's Phase Spectrum depicted on the bottom (Figure 1, bottom). Both are digitized graphs containing 65,536 samples taken with a sample-rate of 44,100 per second. Thus, on the horizontal axis of both graphs there are 65, 536 entries (from 0 to 7 times 10 exp.4). On the vertical axis, the top graph shows magnitudes between 0 and 2 times 10 exp. 8, and the Phase Spectrum graph - bottom- has the ordinates between -π (approximately -3.14), and +π (approximately +3.14).
As can be seen from this example, the Phase Spectrum adds a lot of new information about the noised single note sound, as compared to the magnitude graph (Figure 1, top). The latter is just one peak of a power magnitude located at the main frequency with two side bands of much smaller amplitudes, that in turn are being added to the main tone by noise coming from instrument imperfections.
The information on those two graphs can identify the musical instrument and can be used to characterize its imperfections.
Similarly, applied to other sources of information, the magnitude and the Phase Spectrum can identify the source and/or other characteristics of the information that can be used for added information analyses, its application, and its security.
In order to extract the added information that is contained in the Phase Spectrum, we propose to transform the information's Phase Spectrum into a deterministic function that can serve as a marker for the original information as well as for its Phase Spectrum.
Phase Spectrum Transformation for the Information Marker
The proposed transformation of the Phase Spectrum that will result in the developing of the information marker is as follows:
♦ The range of phase values on the vertical axis (see Figure 1, bottom) is to be subdivided into a discrete set on a given scale, for example by creating 6 subdivisions for positive phases, between 0 and pi (approximately 3.14) radians, and 6 subdivisions for negative phases, between 0 and -pi (approximately -3.14) radians. A total of 13 (including 0 phase) subdivisions (in this example) will be created and identified by 13 horizontal lines superimposed on the Phase Spectrum (Figure 1, bottom).