Fractional Fourier transform(FRFT)is a linear transform generalizing Fourier transform(FT)that plays an important role in the field of signal processing and analysis.FRFT contains an adjustable parameterα,which it ro...Fractional Fourier transform(FRFT)is a linear transform generalizing Fourier transform(FT)that plays an important role in the field of signal processing and analysis.FRFT contains an adjustable parameterα,which it rotates the signal in the time frequency plane and represents the signal in an intermediate domain between time and frequency.FRFT provides a measure about the angular distribution of signal’s energy in time frequency plane.FT is a special case of FRFT when angleαis equal toπ/2.This paper presents mathematical model for obtaining FRFT of PC6 window function.The different parameters of this window function are also obtained with the help of simulation results.A comparison of window function parameters is presented using FT and FRFT.Also comparison of this window function with Hanning window function is presented in terms of Side Lobe Fall off Rate(SLFOR).For different values of FRFT order,PC6 window function shows variation in different parameters.Thus by changing the FRFT order,the minimum stop band attenuation of the resulting window function can be controlled.展开更多
在基于短时傅里叶变换(short-time Fourier transform,STFT)的智能音乐生成系统中,引入梅尔倒谱系数(Mel frequency cepstrum coefficient,MFCC)作为输入特征,并对STFT的损失函数进行优化设计,以提升音乐生成的质量。在对音符输入信号...在基于短时傅里叶变换(short-time Fourier transform,STFT)的智能音乐生成系统中,引入梅尔倒谱系数(Mel frequency cepstrum coefficient,MFCC)作为输入特征,并对STFT的损失函数进行优化设计,以提升音乐生成的质量。在对音符输入信号进行短时傅里叶变换时,需要对时域信号进行截断并添加窗函数,对信号添加时域窗等效于在频域信号中进行卷积。时域信号在截断过程中存在频谱分析误差,使得频谱以实际频率值为中心,以窗函数频谱波形的形状向两侧扩散,从而产生频谱泄漏。不同窗函数的选择对最终生成音乐的品质具有显著影响。为此,提出一种基于能量校正因子、频域最大副瓣和主瓣增益的窗函数分析与选择方法,并开发相应脚本工具,从而完成基于符号域音乐的混合窗函数设计。实验结果表明,混合窗函数在不同的MIDI(musical instrument digital interface)数据集上均可有效减少频谱泄漏对信号截断的影响,具有很好的适应性和灵活性,从而更好地作用于基于STFT的智能音乐生成系统中。展开更多
The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise.The relationship between windowing transform andf...The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise.The relationship between windowing transform andfiltering is analyzed first in the paper.The advantage of adjustable time-frequency window of wavelet transform is introduced.Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed.The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed,and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded.Thirdly,by extending the harmonic wavelet transform,the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper.Then comparing with the Hanning window,the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown,and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented.Finally,the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise,and the satisfactory results are achieved.The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.展开更多
文摘Fractional Fourier transform(FRFT)is a linear transform generalizing Fourier transform(FT)that plays an important role in the field of signal processing and analysis.FRFT contains an adjustable parameterα,which it rotates the signal in the time frequency plane and represents the signal in an intermediate domain between time and frequency.FRFT provides a measure about the angular distribution of signal’s energy in time frequency plane.FT is a special case of FRFT when angleαis equal toπ/2.This paper presents mathematical model for obtaining FRFT of PC6 window function.The different parameters of this window function are also obtained with the help of simulation results.A comparison of window function parameters is presented using FT and FRFT.Also comparison of this window function with Hanning window function is presented in terms of Side Lobe Fall off Rate(SLFOR).For different values of FRFT order,PC6 window function shows variation in different parameters.Thus by changing the FRFT order,the minimum stop band attenuation of the resulting window function can be controlled.
文摘在基于短时傅里叶变换(short-time Fourier transform,STFT)的智能音乐生成系统中,引入梅尔倒谱系数(Mel frequency cepstrum coefficient,MFCC)作为输入特征,并对STFT的损失函数进行优化设计,以提升音乐生成的质量。在对音符输入信号进行短时傅里叶变换时,需要对时域信号进行截断并添加窗函数,对信号添加时域窗等效于在频域信号中进行卷积。时域信号在截断过程中存在频谱分析误差,使得频谱以实际频率值为中心,以窗函数频谱波形的形状向两侧扩散,从而产生频谱泄漏。不同窗函数的选择对最终生成音乐的品质具有显著影响。为此,提出一种基于能量校正因子、频域最大副瓣和主瓣增益的窗函数分析与选择方法,并开发相应脚本工具,从而完成基于符号域音乐的混合窗函数设计。实验结果表明,混合窗函数在不同的MIDI(musical instrument digital interface)数据集上均可有效减少频谱泄漏对信号截断的影响,具有很好的适应性和灵活性,从而更好地作用于基于STFT的智能音乐生成系统中。
基金Project(51675262)supported by the National Natural Science Foundation of ChinaProject(6140210020102)supported by the Advance Research Field Fund Project of ChinaProject(2016YFD0700800)supported by the National Key Research and Development Plan of China
文摘The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise.The relationship between windowing transform andfiltering is analyzed first in the paper.The advantage of adjustable time-frequency window of wavelet transform is introduced.Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed.The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed,and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded.Thirdly,by extending the harmonic wavelet transform,the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper.Then comparing with the Hanning window,the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown,and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented.Finally,the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise,and the satisfactory results are achieved.The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.
