期刊
CMC-COMPUTERS MATERIALS & CONTINUA
卷 67, 期 3, 页码 3983-4003出版社
TECH SCIENCE PRESS
DOI: 10.32604/cmc.2021.014752
关键词
Window functions; Welch method; discrete Fourier transform; spectral leakage
资金
- Ministry of Science and Technology, Taiwan [MOST 104-2221-E-019-026-MY2, MOST 108-2221-E-019-013]
This paper revisits the characteristics of windowing techniques and investigates spectral leakage mitigation using the Welch method. It discusses the role of discrete Fourier transform in digital signal processing and the importance of windowing in spectrum analysis. By selecting appropriate window functions and using the Welch method, noise and spectral leakage can be effectively reduced, enhancing the accuracy of power spectrum estimations.
This paper revisits the characteristics of windowing techniques with various window functions involved, and successively investigates spectral leakage mitigation utilizing the Welch method. The discrete Fourier transform (DFT) is ubiquitous in digital signal processing (DSP) for the spectrum analysis and can be efficiently realized by the fast Fourier transform (FFT). The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed. Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out. Therefore, windowing processing reduces the amplitude of the samples at the beginning and end of the window. In addition to selecting appropriate window functions, a pretreatment method, such as the Welch method, is effective to mitigate the spectral leakage. Due to the noise caused by imperfect, finite data, the noise reduction from Welch's method is a desired treatment. The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio (SNR) is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction. The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected. The design of finite impulse response (FIR) digital filter using the window technique is firstly addressed. The influence of various window functions on the Fourier transform spectrum of the signals is discussed. Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.
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