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The relationship between the number of extrema of compound sinusoidal signals and its high-frequency component | ||
| Journal of Mahani Mathematical Research | ||
| دوره 13، شماره 1 - شماره پیاپی 26، بهمن 2023، صفحه 181-195 اصل مقاله (551.57 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.20128.1327 | ||
| نویسندگان | ||
| Majid Nikzar1، 2؛ Hassan Khotanlou* 1؛ Mirhossein Dezfoulian1 | ||
| 1RIV Lab., Department of Computer Engineering, Bu-Ali Sina University, Hamedan, Iran | ||
| 2Department of Computer Engineering, Yazd University, Yazd, Iran | ||
| چکیده | ||
| As the main findings of our research work, we present a novel theorem on the relationship between the number of extrema of compound sinusoidal signals and its high-frequency component. In the case of signals consisting of the sum of two sine signals, if the high-frequency component has a higher product of the frequency and the amplitude, then we prove that the frequency of the high-frequency component is proportional to the number of extrema in a time interval. This theorem justifies some of the experimental results of other researchers on the relevance of extrema to frequency and amplitude. To confirm the theorem, extrema counting was performed on speech signals and compared with Fourier transform. The experimental results show that the average number of extrema of the compound sinusoidal signal or its derivatives over a time interval can be used to estimate the frequency at its highest frequency band. An important application of this research work is the fast calculation of high frequencies of a signal. This theorem also shows that the number of extrema points can be used as a new effective feature for signal processing, especially speech signals. | ||
| کلیدواژهها | ||
| Extreme points؛ Composite wave؛ Turning points؛ Time-frequency analysis؛ Spectral estimation | ||
| مراجع | ||
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