CAJ | 학술논문

针对噪声背景下计及负频率的 DFT（Discrete Fourier Transform）与 DTFT（Discrete Time Fourier Transform）相位差测量误差问题，用误差理论分别推导出高斯白噪声背景下计及负频率的 DFT 与 DTFT 相位差估计方差计算公式。对不同的泄漏误差系数、采样序列长度及信噪比，在负频率影响条件下进行计算验证。结果表明，仿真结果与计算结果一致，表明相位差测量误差分析公式的正确性。提升频率估计精度、增加采样序列长度、提高信号信噪比，可有效提升计及负频率的 DFT 与 DTFT 相位差测量方法精度。采样序列长度大于2048点或信噪比大于5 dB 时，相位差测量精度提升有限，且 DTFT 相位差测量方法对频率估计精度更敏感。
침대조성배경하계급부빈솔적 DFT（Discrete Fourier Transform）여 DTFT（Discrete Time Fourier Transform）상위차측량오차문제，용오차이론분별추도출고사백조성배경하계급부빈솔적 DFT 여 DTFT 상위차고계방차계산공식。대불동적설루오차계수、채양서렬장도급신조비，재부빈솔영향조건하진행계산험증。결과표명，방진결과여계산결과일치，표명상위차측량오차분석공식적정학성。제승빈솔고계정도、증가채양서렬장도、제고신호신조비，가유효제승계급부빈솔적 DFT 여 DTFT 상위차측량방법정도。채양서렬장도대우2048점혹신조비대우5 dB 시，상위차측량정도제승유한，차 DTFT 상위차측량방법대빈솔고계정도경민감。
Aiming at the errors in phase difference measurement based on DFT(Discrete Fourier Transform)or DTFT (Discrete Time Fourier Transform)methods,taking into account the negative frequency contribution under white noise background,the formulas for evaluating the variance of phase difference were presented according to the error theory.With the consideration of negative frequency contribution,the different leakage error coefficients,sampling sequence lengths and signal-noise-ratios (SNR)were calculated.The results of some the simulations coincide well with those results calculated by using the presented formulas,which shows the correctness of the phase measurement error analysis method.The accuracy of DFT or DTFT based phase difference measurement methods considering the negative frequency contribution could be further improved effectively by enhancing the frequency estimation accuracy,increasing the sampling sequence length,and improving the SNR.When the sampling sequence length is more than 2048 or SNR is greater than 5dB,the further improvement of the accuracy of phase difference measurement is limited.The DTFT based phase measurement method is more sensitive to frequency estimation accuracy.