The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment
Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between th...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-03-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/20/5/1353 |
| _version_ | 1798025495827185664 |
|---|---|
| author | Chao Pan Zhicheng Lv Xia Hua Hongyan Li |
| author_facet | Chao Pan Zhicheng Lv Xia Hua Hongyan Li |
| author_sort | Chao Pan |
| collection | DOAJ |
| description | Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method. |
| first_indexed | 2024-04-11T18:19:38Z |
| format | Article |
| id | doaj.art-4ae67da9a4ae4032b6ce39301e04644e |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-04-11T18:19:38Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-4ae67da9a4ae4032b6ce39301e04644e2022-12-22T04:09:48ZengMDPI AGSensors1424-82202020-03-01205135310.3390/s20051353s20051353The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order MomentChao Pan0Zhicheng Lv1Xia Hua2Hongyan Li3School of Information and Communication Engineering, Hubei University of Economics, Wuhan 430205, ChinaSchool of Information and Communication Engineering, Hubei University of Economics, Wuhan 430205, ChinaSchool of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, ChinaSchool of Information and Communication Engineering, Hubei University of Economics, Wuhan 430205, ChinaNormalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.https://www.mdpi.com/1424-8220/20/5/1353normalized cross-correlationfast algorithmfirst-order momentsystolic arraymultiplication complexity |
| spellingShingle | Chao Pan Zhicheng Lv Xia Hua Hongyan Li The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment Sensors normalized cross-correlation fast algorithm first-order moment systolic array multiplication complexity |
| title | The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment |
| title_full | The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment |
| title_fullStr | The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment |
| title_full_unstemmed | The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment |
| title_short | The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment |
| title_sort | algorithm and structure for digital normalized cross correlation by using first order moment |
| topic | normalized cross-correlation fast algorithm first-order moment systolic array multiplication complexity |
| url | https://www.mdpi.com/1424-8220/20/5/1353 |
| work_keys_str_mv | AT chaopan thealgorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT zhichenglv thealgorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT xiahua thealgorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT hongyanli thealgorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT chaopan algorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT zhichenglv algorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT xiahua algorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment AT hongyanli algorithmandstructurefordigitalnormalizedcrosscorrelationbyusingfirstordermoment |