Digital frequency spectrum analysis based on discrete Fourier transform

Boxuan Tang

doi:10.1117/12.2657431

28 November 2022 Digital frequency spectrum analysis based on discrete Fourier transform

Boxuan Tang

Proceedings Volume 12503, International Conference on Network Communication and Information Security (ICNCIS 2022); 125030F (2022) https://doi.org/10.1117/12.2657431
Event: International Conference on Network Communication and Information Security (ICNCIS 2022), 2022, Qingdao, China

Abstract

Digital frequency spectrum analysis is widely used in signal processing and analyzing, which indicates the physical information and characteristics of components in a signal. According to the Nyquist sampling theorem, a sampling procedure is required to convert a continuous time signal into a discrete time signal, and the sampling rate should be more than twice the signal's maximum frequency. After sampling, windowing is used to truncate the signal and avoid spectrum leakage. Different windows are applied in different situations due to their different function expressions with different characteristics and they have different main lobe width and different side lobe levels. Discrete Fourier Transform (DFT) process is needed to sample the signal after windowing. N-point DFT means sampling X_w(e^jw) with the interval of 2 / π N but the larger N does not guarantee a better performance of DFT signal. Fast Fourier Transform (FFT) is a fast algorithm to calculate the DFT and often used in signal processing technology because of its obvious advantages of small computation and fast calculation. There are two typical functions in MATLAB which carry the FFT sequence with different functions. This paper introduces basic definitions of sampling and using Nyquist sampling theorem to determine sampling rate, compares different window functions and discusses how DFT length effect the frequency spectrum analysis.

Citation Download Citation

Boxuan Tang "Digital frequency spectrum analysis based on discrete Fourier transform", Proc. SPIE 12503, International Conference on Network Communication and Information Security (ICNCIS 2022), 125030F (28 November 2022); https://doi.org/10.1117/12.2657431

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KEYWORDS

Signal processing

Spectrum analysis

Fourier transforms

Digital signal processing

MATLAB

Signal analyzers

Digital filtering

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