#### Effect of Sample Rate on Frequency Values in Sinusoidal Signals

##### Publisher: IEOM Society International
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##### Track: Construction Management

Abstract

Analog signals are generally expressed by sinusoidal waves, where sinusoidal waves are the basis for all forms of analog signals. The important parameters of the sinusoidal signal equation are frequency (fn) and sample rate (fs) which are formulated with the equation x(t) = sin 2?fnt. The time parameter in the t variable in the sinusoidal equation is the duration of data collection for the sinusoidal signal. Frequency data in this study uses two models, namely the first model with a frequency value of f1 = 0.25Hz, f2 = 1.5Hz, f3 = 3Hz and the second model with a frequency value of f1 = 0.25Hz, f2 = 2Hz, f3 = 4.25Hz. The sample rate (fs) used for both models is 8 Hz with a total time duration of 32 seconds. The method used in transforming the time domain of a sinusoidal signal into a frequency domain is using the Discrete Fourier Transform. The results obtained for the first model, namely the reading of the frequency value of f1 = 0.25Hz, f2 = 1.5Hz, f3 = 3Hz can still be read clearly. As for the second model, the frequency value of f1 = 0.25Hz, f2 = 2Hz, f3 = 4.25Hz can still be read. However, a new frequency appears between the frequency readings of f2 = 2Hz and f3 = 4.25 Hz, with a frequency value of f = 3.75Hz. This is because the use of the sample rate (fs = 8 Hz) is smaller than 2 times the signal frequency (2 fn). Therefore, the Nyquist theory in the case study of the second model does not meet the equation fs > 2 fn.

Keywords

Frequency, Sample Rate, Nyquist Theory.

Published in: 3rd South American International Conference on Industrial Engineering and Operations Management

Publisher: IEOM Society International
Date of Conference: May 10-12, 2022

ISBN: 978-1-7923-9159-0
ISSN/E-ISSN: 2169-8767