Multiple Aliasing of Windowed Real-Valued Signal as a Cause of Accuracy Limitation of DFT Methods

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F26%3A00564171" target="_blank" >RIV/60162694:G43__/26:00564171 - isvavai.cz</a>

Výsledek na webu

<a href="https://dx.doi.org/10.1109/ACCESS.2025.3526325" target="_blank" >https://dx.doi.org/10.1109/ACCESS.2025.3526325</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/ACCESS.2025.3526325" target="_blank" >10.1109/ACCESS.2025.3526325</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Multiple Aliasing of Windowed Real-Valued Signal as a Cause of Accuracy Limitation of DFT Methods

Popis výsledku v původním jazyce

DFT spectral signal analysis is a widely used method for various types of signal processing due to its several advantages. In the case of incoherently sampled real-valued signals, spectral leakage and aliasing occur, causing errors in the signal spectrum estimate. Standard techniques consider that negative spectral leakage components influence the positive part of the spectrum by aliasing. Consequently, these methods are trying to suppress these spectral components. The paper shows that this way may not be satisfactory, because windowing of the signal, necessarily associated with the use of DFT, causes the appearance of repetitive bands in addition to the considered negative mirror components. These components cause additional aliasing, albeit with a decreasing but non-negligible influence, causing further errors in the calculated spectral components. This effect of multiple aliasing, which has not been considered so far, explains the limited maximum achievable accuracy of commonly used DFT methods. The paper further explains that the effect of the random part of such multiple aliasing can be fully compensated converting the real-valued signal to its analytic counterpart. Then the permanent part of the multiple aliasing can be simply eliminated from the obtained analytic signal. Furthermore, the paper introduces a simple procedure for converting real-valued sinusoidal signal to analytic signal in time domain. This procedure is used to develop a new frequency estimation method with minimal estimation error even for very small numbers of signal samples. By using a rectangular window, it minimizes the effect of noise practically to the Cramer-Rao bound.

Název v anglickém jazyce

Multiple Aliasing of Windowed Real-Valued Signal as a Cause of Accuracy Limitation of DFT Methods

Popis výsledku anglicky

DFT spectral signal analysis is a widely used method for various types of signal processing due to its several advantages. In the case of incoherently sampled real-valued signals, spectral leakage and aliasing occur, causing errors in the signal spectrum estimate. Standard techniques consider that negative spectral leakage components influence the positive part of the spectrum by aliasing. Consequently, these methods are trying to suppress these spectral components. The paper shows that this way may not be satisfactory, because windowing of the signal, necessarily associated with the use of DFT, causes the appearance of repetitive bands in addition to the considered negative mirror components. These components cause additional aliasing, albeit with a decreasing but non-negligible influence, causing further errors in the calculated spectral components. This effect of multiple aliasing, which has not been considered so far, explains the limited maximum achievable accuracy of commonly used DFT methods. The paper further explains that the effect of the random part of such multiple aliasing can be fully compensated converting the real-valued signal to its analytic counterpart. Then the permanent part of the multiple aliasing can be simply eliminated from the obtained analytic signal. Furthermore, the paper introduces a simple procedure for converting real-valued sinusoidal signal to analytic signal in time domain. This procedure is used to develop a new frequency estimation method with minimal estimation error even for very small numbers of signal samples. By using a rectangular window, it minimizes the effect of noise practically to the Cramer-Rao bound.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

IEEE ACCESS

ISSN

2169-3536

e-ISSN

2169-3536

Svazek periodika

13

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

6515-6526

Kód UT WoS článku

001397806100026

EID výsledku v databázi Scopus

2-s2.0-85214907584