Abstract
In this paper, a modified sampling rate, which is smaller than the usual Nyquist rate, is determined for bandlimited signals using a method like single side band (SSB-like). SSB-like method is characterized using the base signal of single side band Amplitude Modulation (SSB-AM) instead of the actual AM signal. The sampling should be performed on the base SSB signal, which is a complex valued signal. That is, SSB-like sampling is performed on a complex valued signal with a corresponding Nyquist frequency which is half of the actual required sampling frequency. Also, a theoretical sampling method is proposed as a theorem that results in sampled values based on the mathematical properties of transformations. The proposed complex sampling method is novel in the context of sampling and valid for any band-limited real valued signal. The application of the method to real physical cases and a block diagram for complex sampling is under study.
References
- [1] C. E. Shannon, “Communication in the Presence of Noise,” Proc. of IRE, vol. 37, pp. 10–21, Jan. 1949. Reprinted in Proc. of IEEE, vol.86, pp.447-457 no.2 Feb. 1998.
- [2] C. L. Philips and H. T. Nagle, Digital Control System Analysis and Design, 3rd Ed. Prentice Hall, 1994.
- [3] S. Haykin, and M. Moher, Communication Systems, 5th Ed. John Wiley and Sons, 2009.
- [4] Fischer, Jens V. and Rudolf L. Stens. “On Inverses of the Dirac Comb.” MDPI Mathematics, (2019). DOI:10.3390/math7121196
- [5] J. B. Anderson, F. Rusek and V. Öwall, "Faster-Than-Nyquist Signaling," in Proceedings of the IEEE, vol. 101, no. 8, pp. 1817-1830, Aug. 2013, doi: 10.1109/JPROC.2012.2233451.
- [6] Oppenheim, Alan V.; Willsky, Alan S. and Hamid, Nawab S., Signals and Systems, (Prentice-Hall series in Signal Processing) Pearson, 1996.
- [7] Canbolat, H., (2024) “Reconstruction of a Band Limited Signal Sampled Slower than the Nyquist Rate Using AM Modulated Version of the Signal.” J. of Engineering and Applied Sciences Technology. SRC/JEAST-394. DOI: doi.org/10.47363/JEAST/2024(6)276
- [8] H. Canbolat, “A Modified Sampling Rate for a Continuous Sampling using Dirac Comb”, ELECO2024 (Proc. National Conf. on EE and Biomedical Eng.), Bursa, Türkiye, November 2024. DOI: 10.1109/ELECO64362.2024.10847200
- [9] H. Canbolat, “Amplitude Modulation as a Pole-placement Problem”, TOK2024 Automatic Control National Meeting, Konya, Türkiye, pp. 801-805 September 2024.
- [10] D. K. Weaver, "A Third Method of Generation and Detection of Single-Sideband Signals," in Proceedings of the IRE, vol. 44, no. 12, pp. 1703-1705, Dec. 1956, doi: 10.1109/JRPROC.1956.275061.
- [11] K. Martin, “Complex Signal Processing is Not-Complex”, available on https://www.mikrocontroller.net/attachment/151612/complex_signals.pdf
- [12] P. Driessen, “ECE350 Textbook Fall 2020”, available on https://mistic-lab.github.io/ece-communications-labs/_docs/pdriessen_textbook.pdf
Abstract
In this paper, a modified sampling rate, which is smaller than the usual Nyquist rate, is determined for bandlimited signals using a method like single side band (SSB-like). SSB-like method is characterized using the base signal of single side band Amplitude Modulation (SSB-AM) instead of the actual AM signal. The sampling should be performed on the base SSB signal, which is a complex valued signal. That is, SSB-like sampling is performed on a complex valued signal with a corresponding Nyquist frequency which is half of the actual required sampling frequency. Also, a theoretical sampling method is proposed as a theorem that results in sampled values based on the mathematical properties of transformations. The proposed complex sampling method is novel in the context of sampling and valid for any band-limited real valued signal. The application of the method to real physical cases and a block diagram for complex sampling is under study.
References
- [1] C. E. Shannon, “Communication in the Presence of Noise,” Proc. of IRE, vol. 37, pp. 10–21, Jan. 1949. Reprinted in Proc. of IEEE, vol.86, pp.447-457 no.2 Feb. 1998.
- [2] C. L. Philips and H. T. Nagle, Digital Control System Analysis and Design, 3rd Ed. Prentice Hall, 1994.
- [3] S. Haykin, and M. Moher, Communication Systems, 5th Ed. John Wiley and Sons, 2009.
- [4] Fischer, Jens V. and Rudolf L. Stens. “On Inverses of the Dirac Comb.” MDPI Mathematics, (2019). DOI:10.3390/math7121196
- [5] J. B. Anderson, F. Rusek and V. Öwall, "Faster-Than-Nyquist Signaling," in Proceedings of the IEEE, vol. 101, no. 8, pp. 1817-1830, Aug. 2013, doi: 10.1109/JPROC.2012.2233451.
- [6] Oppenheim, Alan V.; Willsky, Alan S. and Hamid, Nawab S., Signals and Systems, (Prentice-Hall series in Signal Processing) Pearson, 1996.
- [7] Canbolat, H., (2024) “Reconstruction of a Band Limited Signal Sampled Slower than the Nyquist Rate Using AM Modulated Version of the Signal.” J. of Engineering and Applied Sciences Technology. SRC/JEAST-394. DOI: doi.org/10.47363/JEAST/2024(6)276
- [8] H. Canbolat, “A Modified Sampling Rate for a Continuous Sampling using Dirac Comb”, ELECO2024 (Proc. National Conf. on EE and Biomedical Eng.), Bursa, Türkiye, November 2024. DOI: 10.1109/ELECO64362.2024.10847200
- [9] H. Canbolat, “Amplitude Modulation as a Pole-placement Problem”, TOK2024 Automatic Control National Meeting, Konya, Türkiye, pp. 801-805 September 2024.
- [10] D. K. Weaver, "A Third Method of Generation and Detection of Single-Sideband Signals," in Proceedings of the IRE, vol. 44, no. 12, pp. 1703-1705, Dec. 1956, doi: 10.1109/JRPROC.1956.275061.
- [11] K. Martin, “Complex Signal Processing is Not-Complex”, available on https://www.mikrocontroller.net/attachment/151612/complex_signals.pdf
- [12] P. Driessen, “ECE350 Textbook Fall 2020”, available on https://mistic-lab.github.io/ece-communications-labs/_docs/pdriessen_textbook.pdf
Details
| Primary Language | English |
|---|---|
| Subjects | Electrical Engineering (Other) |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | July 22, 2025 |
| Publication Date | July 31, 2025 |
| Submission Date | April 2, 2025 |
| Acceptance Date | April 21, 2025 |
| Published in Issue | Year 2025 Volume: 9 Issue: 1 |
