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 transfor...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 efciently 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,nite 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 nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence 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.展开更多
基金supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 104-2221-E-019-026-MY2 and MOST 108-2221-E019-013].
文摘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 efciently 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,nite 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 nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence 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.
