Estimating frequency by interpolation using Fourier coefficients

The periodogram of a time series that contains a sinusoidal component provides a crude estimate of its frequency parameter, the maximizer over the Fourier frequencies being within O(T^-1) of the frequency as the sample size T increases. In the paper, a technique for obtaining an estimator that has root mean square error of order T ^-3/2 is presented, which involves only the Fourier components of the time series at three frequencies, The asymptotic variance of the estimator varies between, roughly, the asymptotic variance of the maximizer of the periodogram over all frequencies (the Cramer-Rao lower bound) and three times this variance. The advantage of the new estimator is its computational simplicity     

Study on frequency estimation based on weighted least square method with three Fourier coefficients

In this paper, a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method. Based on the idea of Provencher, three biggest Fourier coefficients in the maximum periodogram are considered, the Fourier coefficients can be written as three equations about the amplitude, phase, and frequency, and the frequency is estimated by solving equations. Because of the error of measurement, weighted least square method is used to solve the frequency equation and get the signal frequency. It is shown that the proposed estimator can approach the Cramer-Rao Bound （CRB） with a low Signal-to-Noise Ratio （SNR） threshold and has a higher accuracy.     

Fast frequency estimation and tracking using Lagrange interpolation

A computationally efficient and accurate frequency estimation and tracking algorithm is proposed, based on the adaptive frequency estimator (AFE) of Etter and Hush. A Lagrange interpolator (a fractional delay filter) is used to estimate the gradient of the performance surface of the adaptation, which enables highly accurate estimation. The performance of the new algorithm is demonstrated in the context of tracking a chirp signal in noise     

Iterative inter-lattice interpolation

The author introduces an iterative algorithm for interpolating an image when the sampling lattice is not uniform, but differs from block to block. This technique may find applications in adaptive sub-sampling for image coding     

一种基于CRS插值的频偏估计方法

针对正交频分复用系统对频率偏移异常敏感导致接收机无法正确解调信号的问题,提出了一种小区特定参考信号(Cell-special Reference Signal,CRS)改进的频偏估计方法。首先,对发送的CRS与接收的CRS进行互相关运算,得到信道估计值;然后,对CRS在频域进行插值,使得每个时隙中不同OFDM符号对应子载波位置的参考信号相同;最后,对两个不同OFDM符号中的参考信号部分进行相关性运算,求出频偏。与基于CRS的频偏估计方法相比,该方法用信道估计值做互相关运算,消除了噪声和多径干扰带来的影响;通过对CRS进行插值,提高了频偏估计精度;通过减小计算相关性的两OFDM符号间的距离,使频偏估计范围由\[-1 kHz,1 kHz\]扩大到\[-1.75 kHz,1.75 kHz\]。     

Iterative methods based on polynomial interpolation filters to detect discontinuities and recover point values from Fourier data

In previous papers, we proposed new filters based on polynomial interpolation to approximate the point values of a piecewise smooth function f on [0,1] from its Fourier coefficients and derived error estimates. We proved that if all the discontinuity points of f are nodes, we can reconstruct point values of f accurately, even close to the discontinuities. We use the new filters to develop iterative methods for detecting the discontinuity points and, therefore, accurately approximate the point values of the function from its Fourier coefficients.     

一种新的极高精度的T_IIN频率估计内插算法

针对多普勒条件下接收端复信号的频率估计难的问题,研究了一种基于离散傅里叶变换与迭代频率估计的内插综合算法.区别于经典的内插算法,新算法在迭代频率内插算法基础上充分利用复数快速傅里叶变换结果的实虚部值,并通过最大峰值频谱和相邻两侧谱线以极高精度内插估计出复信号的频率参数.仿真结果分析表明,在二次迭代条件下信噪比为-10 dB时,该算法估计均方根误差仍能逼近克拉美-罗限的1.0021倍.该算法在同等条件下比经典的Rife、Quinn和IIN算法具有更高的准确性、稳定性和可靠性.     

Measuring frequency response of dispersion compensating fibre Bragg grating using Fourier coefficients

Based on a double modulation method, the amplitude and phase responses of a dispersion compensating grating are measured using the complex Fourier coefficients of a periodic signal and a high-resolution optical spectrum analyser.     

基于短时傅立叶变换的跳频序列瞬时频率估计

采用了G函数的方法来模拟跳频序列，然后利用短时傅立叶变换对它进行分析与瞬时频率的估计。该方法能够有效地描绘出跳频信号的频率随时间跳变的规律（跳频图案），具有很高的时间一频率分辨率。计算机仿真验证了应用短时傅立叶变换分析跳频序列的有效性和实用性。     

Accurate frequency estimation using an all-pole filter with mostly zero coefficients

An all-pole Lth order filter with only M (M < L) nonzero coefficients is used to estimate accurately the frequencies of M closely spaced sinusoidal signals in noise. The method eliminates redundancy in the linear prediction equations which caused the spurious spectral peaks observed in previously known methods [3], [4]. Since most filter coefficients are zero, the computational effort required is small.     

Coarse frequency estimation using the discrete Fourier transform (Corresp.)

The discrete Fourier transform (DFT) is applied as a coarse estimator of the frequency of a sine wave in Gaussian noise. Probability of anomaly and the variance of the estimation error are determined by computer simulation for several DFT block sizes as a function of signal energy-to-noise density ratiomathcal{E}/N_0. Several data windows are considered, but uniform weighting gives the best performance.     

Iterative frequency domain channel estimation for dft-precoded ofdm systems using in-band pilots

We consider two techniques of in-band frequency domain multiplexed (FDM) pilots using interleaved frequency domain multiple access (IFDMA) signal with a Chu sequence for DFT-precoded OFDM (or single-carrier (SC)) systems. One, called frequency domain superimposed pilot technique (FDSPT), superimposes pilot tones onto scaled or deleted data tones, which preserves spectral efficiency at the expense of a slight performance loss. The other, called frequency expanding technique (FET), multiplexes pilot tones by displacing data tones, which slightly reduces spectral efficiency. Using FDM pilots in SC systems facilitates flexible and efficient assignment of signals to available spectrum. We propose an iterative frequency domain decision-directed interference cancellation technique to reduce the intersymbol interference level of SC signals with FDSPT pilots (resulting from the suppression of data tones). Moreover, we propose a low complexity frequency domain iterative decision-directed channel estimation (IDDCE) technique for SC systems using FDM pilots. Using IDDCE, the frame error rate (FER) performance for coded SC systems using FET and FDSPT pilots with interference cancellation is found to be about 0.2 dB and about 0.5 dB, respectively, away from the FER performance with known channel frequency response at FER=10^-2. FDSPT pilots can also be used for OFDM systems with channel coding. It is found that an extra 1 dB of SNR is required at FER=10^-2,compared with that using the conventional FET pilots for OFDM systems.     

Calculating Fourier coefficients for Chebyshev patterns by recurrence formulas

Two recurrence schemes are given for finding Amin Tn(ax + b) = Σm=0ⁿAmTm(x) for given n, a, and b, where Tm(x)= cos (m arccos x). This problem arises in the calculation of feeding coefficients to produce optimum beam patterns in the design of certain linear arrays.     

基于离散傅里叶变换的高动态突发信号检测及频率估计

针对高动态突发通信应用环境,提出了一种新的基于频率域的突发信号检测及载波频偏估计算法,通过一次离散傅里叶变换( DFT)实现突发信号存在性检测及频率估计,并与经典Power-Law算法进行了比较。仿真结果表明：在低信噪比条件下,新算法检测信噪比门限改善超过1 dB,频率估计均方根误差小于符号率的1‰,并且对载波频偏及信号电平动态不敏感,实现结构简单,适合实时处理及工程应用。     

Super-resolution reconstruction based on linear interpolation of wavelet coefficients

High resolution image reconstruction is an image process to reconstruct a high resolution image from a set of blurred, degraded and shifted low resolution images. In this paper, the reconstruction problem is treated as a function approximation. We use linear interpolation to build up an algorithm to obtain the relationship between the detail coefficients in wavelet subbands and the set of low resolution images. We use Haar wavelet as an example and establish the connection between the Haar wavelet subband and the low resolution images. Experiments show that we can use just 3 low resolution images to obtain a high resolution image which has better quality than Tikhonov least-squares approach and Chan et al. Algorithm 3 in low noise cases. We also propose an error correction extension for our method which can lead to very good results even in noisy cases. Moreover, our approach is very simple to implement and very efficient.     

Nonuniform fast Fourier transforms using min-max interpolation

The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.     

用迭代傅里叶变换算法实现光学分级图像加密

在虚拟光学数据加密理论的基础上,基于光学4f系统及迭代傅里叶变换算法(IFTA),提出利用多个相位板进行分级图像加密的方法,将不同密级的图像分别加密到不同的相位板中,给出其理论原理和实现方法,并通过计算机模拟验证了该方法的有效性。在解密过程中,利用不同数目的相位板可以得到不同图像,相位板越多,得到的图像也就越多。随着相位板数目的增加,要想得到正确的解密图像,相位板放置的次序也有严格要求,系统的安全性也因此大大提高。此方法可将信息进行分级加密,用于对不同权限级别的用户开放,也可用于安全认证和准入检查系统。     

雷达散射截面基于MBPE模型的在频空两域的双内插

Padé多项式模型一般被用于频域上的模基参数估计 ( MBPE) ,为了将空域信息卷入拟合公式 ,混合的 MBPE技术采用了 Padé多项式和单项式或多项式相结合的方法以便同时在频域和空域进行双内插。这种技术已在天线中得到应用 ,此文将该技术应用于雷达散射截面 ( RCS)领域。为了得到更高的精度和更快的计算机处理时间 ,采用了将大矩阵分块计算 ,空频域分区内插 ,以及自适应算法等方法