Showing papers on "Discrete-time Fourier transform published in 2020"

Accurate Frequency Estimator of Sinusoid Based on Interpolation of FFT and DTFT

Abstract: An accurate frequency estimator of complex sinusoid in additive white noise is proposed. It is based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT). Zero-padding is firstly performed before the FFT of the sinusoid sampled data, and the coarse estimate is obtained by searching the discrete frequency index of the maximum FFT spectrum line. Then the fine estimate is obtained by employing the maximum FFT spectrum line and two DTFT sample values located on the left and right side of the maximum spectrum line. The correlation coefficients between the Fourier Transform of the noises on two arbitrarily spaced spectrum lines are derived, and the MSE calculation formula is derived in additive white noise background based on the correlation coefficients. Simulations results demonstrate that the proposed algorithm has lower MSE than the competing algorithms, and its signal-to-noise ratio (SNR) threshold is lower compared with Candan algorithm, AM algorithm and Djukanovic algorithms.

Turing Computability of Fourier Transforms of Bandlimited and Discrete Signals

Abstract: The Fourier transform is an important operation in signal processing. However, its exact computation on digital computers can be problematic. In this paper we consider the computability of the Fourier transform and the discrete-time Fourier transform (DTFT). We construct a computable bandlimited absolutely integrable signal that has a continuous Fourier transform, which is, however, not Turing computable. Further, we also construct a computable sequence such that the DTFT is not Turing computable. Turing computability models what is theoretically implementable on a digital computer. Hence, our result shows that the Fourier transform of certain signals cannot be computed on digital hardware of any kind, including CPUs, FPGAs, and DSPs. This also implies that there is no symmetry between the time and frequency domain with respect to computability. Therefore, numerical approaches which employ the frequency domain representation of a signal (like calculating the convolution by performing a multiplication in the frequency domain) can be problematic. Interestingly, an idealized analog machine can compute the Fourier transform. However, it is unclear whether and how this theoretical superiority of the analog machine can be translated into practice. Further, we show that it is not possible to find an algorithm that can always decide for a given signal whether the Fourier transform is computable or not.

Generalized gaussian bounds for discrete convolution powers

Abstract: We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is a trigonometric rational function, which generalizes previous results that were restricted to trigonometric polynomials. We also allow the modulus of the Fourier transform to attain its maximum at finitely many points over a period.

An Accurate and Efficient Frequency Estimation Algorithm by Using FFT and DTFT

Abstract: In this paper, a new algorithm of sinusoidal signal frequency estimation based on interpolation of Fast Fourier Transform (FFT) and Discrete-Time Fourier Transform (DTFT) is proposed. Firstly, A-point FFT is used to search the position of the maximum FFT spectrum line and get the rough frequency estimation. Then three DTFT spectrum lines located at any position within the main lobe is used to obtain the fine frequency estimation value. Next, in order to further improve the estimation performance, the proposed algorithm is combined with Candan algorithm. According to the simulation results, Root Mean Square Error (RMSE) of the proposed algorithm is significantly lower than Candan algorithm, RCTSL algorithm and A&M algorithm. In a wide range of Signal-to-Noise Ratio (SNR), the proposed algorithm is closer to the Cramer-Rao lower bound (CRLB) than the competitive algorithms. In terms of computation complexity, the proposed algorithm in this paper is lower than A&M algorithm, HAQSE algorithm and RCTSL algorithm.

Study of Blockage Diagnosis for Hydrocyclone Using Vibration-Based Technique Based on Wavelet Denoising and Discrete-Time Fourier Transform Method

Abstract: Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a lab-scale hydrocyclone using a vibration-based technique based on wavelet denoising and the discrete-time Fourier transform method. The results indicate that the farther away the installation location from feed inlet the more regular the frequency is, which reveals that the installation plane near to the spigot generated the regular frequency distribution. Furthermore, the acceleration amplitude under blockage degrees 0%, 50% and 100% fluctuates as a sine shape with increasing time, meanwhile the vibration frequency of the hydrocyclone rises with increasing throughput. Moreover, the distribution of four dimensional and five non-dimensional parameters for the time domain shows that the standard deviation, compared to the others, reduced gradually with increases in blockage degree. Thus, the standard deviation was used to evaluate the online diagnosis of the blockage. The frequency domain distribution under different throughput reveals that the characteristic peaks consisting of the faulty frequency and multiple frequency were produced by the faulty blockage and the feed pump, respectively. Hence, the faulty peak of 16–17 Hz was adopted to judge the real-time blockage of the hydrocyclone, i.e., the presence of the characteristic peak marks the blockage, and its value is proportional to the blockage degree. The application of the online monitoring system demonstrates that the combination of the time domain and the frequency domain could admirably detect the running state and rapidly recognize blockage faults.

Hilbert Envelope Extraction from Real Discrete Finite Signals Considering the Nonlocality of Hilbert Transform

Abstract: Methods of determining the envelope (instantaneous amplitude) of a real signal for continuous and discrete cases are investigated. The analysis of advantages and disadvantages of existing methods for extraction the envelope of a real signal for continuous and discrete cases are given. The efficiency of the choice of determining the conjugate signal by Hilbert transform method is substantiated. The problem of determining Hilbert envelope for real, discrete and finite signals by the methods of discrete Fourier transform (DFT) and discrete-time Fourier transform (DTFT) is considered. The reason for the large relative errors in the measurement of Hilbert envelopes by DFT method is revealed. A new effective method and an effective method for measuring the envelope of a real, discrete, finite signal is developed, which reduces the relative error of its measurement by an order of magnitude and reduces by an order of magnitude the computational cost and the necessary memory for implementing the method as well. The theoretical results obtained in the work are confirmed by the results of numerical modeling.

Determining the Envelope of Real Finite Discrete Signal via Parametric Discrete Fourier Transform

Abstract: the purpose of the work is to develop a novel method for determining the envelope of a real finite discrete vibro-acoustic signal (RFDVS), given on a finite interval. The novel method must be free from the disadvantages of methods based on discrete Fourier transform and discrete-time Fourier transform. A brief review of the advantages of vibro-acoustic functional diagnostics over other diagnostic methods of the technical condition of machines is carried out. The role of envelopes of vibro-acoustic signal in the functional diagnosis of objects is considered. The article investigates the methods for determining the envelope (instantaneous amplitude) of RFDVS, both in the time and in the frequency domain. Analysis of the advantages and disadvantages of the Hilbert envelopes, determined respectively on the basis of discrete Fourier transform (DFT) and discrete-time Fourier transform (DTFT) is given. The main reason for the large relative error in measuring the Hilbert envelope by DFT method in comparison with the measurement of Hilbert envelopes by DTFT method is revealed. A generalization of DFT in the form of parametric discrete Fourier transform (DFT-P) is given, and the analytical properties of DFT and DFT-P are compared. Fast algorithms for computing DFT-P are proposed parametric fast Fourier transform (FFT-P) algorithms. Based on DFT-P, implemented by the FFT-P, a novel method for determining the envelope of a compact discrete vibro-acoustic signal has been developed. The effectiveness and efficiency of the developed method of extracting the envelope is proved. Application of the proposed method allows one to reduce the relative error of envelope extracting by an order of magnitude, and reduce the computational cost and the required memory of the processor facility instrumentation by an order of magnitude. The theoretical results obtained in the work are confirmed by the results of numerical simulation of the measurement of the envelope of a real finite discrete signal by the known and proposed method, as well as by experiment on real vibro-acoustic signal.

On Derivation of Discrete Time Fourier Transform from Its Continuous Counterpart

Abstract: This paper is devoted to some problems that appear in derivations of the discrete time Fourier transform from a formula for its continuous time counterpart for transformation from the time into the frequency domain as well as to those regarding transformation in the inverse direction. In particular, the latter ones remained so far an unresolved problem. It is solved for the first time here. Many detailed explanations accompanying the solution found are presented. Finally, it is also worth noting that our derivations do not exploit any of such sophisticated mathematical tools as the so-called Dirac delta and Dirac comb.

An Accurate Frequency Estimation Algorithm by Using DFT and Cosine Windows

Abstract: Sinusoidal signal frequency estimation is one of the fundamental problems in signal processing, and it is widely used in wireless communication, signal processing, navigation, radar and so on In this paper, an interpolation frequency estimation algorithm based on Discrete Fourier Transform (DFT) and cosine windows is proposed Firstly, the sampling sequence of the signal is multiplied by a cosine window Then, N-point DFT is used to search the position of the maximum spectral line and get the coarse estimation of frequency Finally, the accurate frequency estimation is obtained by DFT interpolation of the maximum spectral line and the two Discrete-Time Fourier Transform (DTFT) samples on the left and right of the maximum spectral line According to the simulation results, the performance of the proposed algorithm is better than that of MV-IpDTFT(3) algorithm, MV-IpDTFT(2) algorithm and Candan algorithm The effect of harmonic interference on the frequency estimation results can be effectively suppressed

Infinite Sequences, Series Convergence and the Discrete Time Fourier Transform over Finite Fields.

Abstract: Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite field Fourier transform (FFFT). A finite field version of the DTFT is introduced and the FFFT is redefined with a complex kernel, which makes it a more appropriate finite field version of the Discrete Fourier Transform. These transforms can handle FIR and IIR filters defined over finite algebraic structures.

Positioning method based on frequency domain analysis and convolutional neural network

Abstract: The invention discloses a positioning method based on frequency domain analysis and a convolutional neural network. The method comprises the steps: based on an accelerometer and a gyroscope in a carrier inertia measurement unit, generating a spectrogram of discrete time signals through discrete time Fourier transform, designing a convolutional neural network, acquiring the pose transformation of acarrier by mining high latitude characteristics in the spectrogram, and then achieving the carrier positioning. According to the method, under the condition that the type and the position of a sensorcarrier are not limited, only original inertial measurement unit data is sent to the neural network in a sliding window mode, and the positioning function can be accurately and robustly achieved.

Cyclotomic Fast Fourier Transform with Reduced Additive Complexity

Abstract: The Fourier transform is a standard system analysis tool for viewing the frequency content of a signal. The Fourier transform of a sequence, commonly referred to as the discrete time Fourier transform. Discrete Fourier Transforms are implemented through efficient fast Fourier Transform (FFT) algorithms. For Finite field special algorithms are constructed. Based on findings very useful method for the working of Fourier Transform over finite field was developed called Cyclotomic fast Fourier Transform (CFFT). The algorithm has less multiplicative complexity, but additive complexity is very high. The main aim of the research paper is to design Cyclotomic fast Fourier Transform with reduced additive complexity. Proposed algorithm reduces common summands in the Multiple Constant Multiplications. The approach used in algorithm is search for occurances identical expressions and replace it with new single variable.The algorithm is advantageous as it resulted in additive complexity reduction, computation of area of constant matrix multiplication with minimum complexity. The presented method is critically compared with existing method and the experimental result shows that the algorithm satisfies less additive complexity with less number of Xor gates.

Classification of 12-lead ECGs Using Intra-Heartbeat Discrete-time Fourier Transform and Inter-Heartbeat Attention

Abstract: In this work, we built a model to classify 12-lead ECGs using attention for the PhysioNet/Computing in Cardiology Challenge 2020. Since information about different classification outcomes might be present only in specific segments, we tune our feature representation to show the frequency distribution shift as we move through time. This is done by first representing the original signal as a spectrogram, which shows the signal's frequency spectrum during different time windows (heartbeats). The frequency spectrum at each heartbeat is extracted using discrete-time Fourier transform. The spectrogram is then inputted to a bidirectional LSTM network where each heartbeat vector represents a time step. The outputs of the bidirectional LSTM network at each stage are then used as attention vectors. The attention vectors are then multiplied with the original signal window embeddings, which are used to generate the final output. Our approach achieved a challenge validation score of 0.416 and a test score of 0.024 but were not ranked due to omissions in the submission (team name: SBU_AI).

Method and apparatus for the reception of a signal

Abstract: A method for the reception of a frequency hopped direct sequence spread spectrum signal includes acquiring the signal by splitting the received signal into a plurality of processing sub-channels, each corresponding to one or more hop frequencies; and within each sub-channel: i) subtracting any sub-carrier frequency from the received signal; ii) filtering the signal from (i) using a chip-matched filter; iii) selecting a sub-set of samples from the filtered signal; iv) correlating the sampled signal from step (iii) with a known reference signal to produce at least one correlator output. The output(s) from each sub-channel are provided to an input of a corresponding one or more common discrete time Fourier transforms (DTFT), and an output therefrom having a peak above a predetermined threshold is selected for further processing in the receiver. The method is a less expensive way of tracking the signal and can demodulate appropriately modulated signals.

A New Image Hashing based on Discrete Trinion Fourier Transform

Abstract: In this paper, a new robust image hashing scheme is proposed base on discrete trinion Fourier transform(DTFT). The key features of the present scheme rely on (i) The DTFT provides an effective way to jointly deal with the three channels of color images. (ii) The final hash is generated according to the amplitudes of these DTFT coefficients. (iii) Scrambling is applied at the last stage of hash generation to enhance the system security. The experiment results show that the proposed method offers good robust to most image content preserving operations and have good discrimination performance.