A Method For Fine Resolution Frequency Estimation From Three DFT Samples

The parameter estimation of a complex exponential waveform observed under white noise is typically tackled in two stages. In the first stage, a coarse frequency estimate is found by the application of an N-point DFT to the input of length N. In the second stage, a fine search around the peak determined in the first stage is conducted. The method proposed in this paper presents a simpler alternative. The method suggests a nonlinear relation involving three DFT samples already calculated in the first stage to produce a real valued, fine resolution frequency estimate. The estimator approaches Jacobsen's estimator for large N and presents a bias correction which is especially important for small and medium values of N.


A fine-resolution frequency estimator using an arbitrary number of DFT coefficients
Orguner, Umut; Candan, Çağatay (2014-12-01)
A method for the frequency estimation of complex exponential signals observed under additive white Gaussian noise is presented. Unlike competing methods based on relatively few Discrete Fourier Transform (DFT) samples, the presented technique can generate a frequency estimate by fusing the information from all DFT samples. The estimator is shown to follow the Cramer-Rao bound with a smaller signal-to-noise ratio (SNR) gap than the competing estimators at high SNR.
An efficient method for fundamental frequency estimation of periodic signals with harmonics
Çelebi, Utku; Candan, Çağatay; Department of Electrical and Electronics Engineering (2020-8)
A computationally efficient method for the fundamental frequency estimation of a group of harmonically related complex sinusoids is given. To this aim, an efficient frequency estimation method for single tone complex sinusoids is adapted to the harmonic frequency estimation problem. The main idea of the suggested Fast Fourier Transform based method is the frequency estimation of individual complex sinusoids after the removal of the interference due to other harmonics. After several iterations of estimation ...
A novel two-step pseudo-response based adaptive harmonic balance method for dynamic analysis of nonlinear structures
Sert, Onur; Ciğeroğlu, Ender (Elsevier BV, 2019-09-01)
Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is great...
On the Implementation of Optimal Receivers for LFM Signals using Fractional Fourier Transform
Candan, Çağatay (2008-05-30)
We present a novel receiver structure for the detection and parameter estimation of linear frequency modulated signals. The proposed structure is based on the relations between the fractional Fourier transform and the ambiguity function. It has been shown that the optimal ML receiver, which is the peak detector in the ambiguity plane, can be implemented at a reduced search complexity with the proposed method. The proposed method uses two 1-dimensional search operations in two different fractional Fourier do...
An Accurate and Efficient Two-Stage Channel Estimation Method Utilizing Training Sequences with Closed Form Expressions
Candan, Çağatay (2011-12-01)
A novel two-stage frequency domain channel estimation method especially suitable for the estimation of long channels such as ultra wide band channels is proposed. The proposed method can efficiently use the sequences with closed form analytical expressions such as the Legendre sequences. (The suggested method does not require a computationally intense search for good training sequences which is infeasible for long training sequences.) The method is shown to present a minor improvement in the total estimatio...
Citation Formats
Ç. Candan, “A Method For Fine Resolution Frequency Estimation From Three DFT Samples,” IEEE SIGNAL PROCESSING LETTERS, pp. 351–354, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39671.