Discrete Fourier Transform Operation Research Articles

Analysis of application of FFT in quantum field

The algorithm concept of fast Fourier transform, Heisenberg uncertainty, and the combination of the two are expounded. Fast Fourier Transform (FFT) is not a new discrete Fourier Transform, but a fast algorithm for Discrete Fourier Transform (DFT). For a long time, the DFT was not really used because of the large amount of computation, even if it was used by computers, it was difficult to deal with problems in real time. It was not until when Cooley and Key first proposed a fast algorithm for DFT operations, and later, when fast algorithms by G. Sullivan and. Key appeared in succession, that fundamental changes took place. People began to realize some inherent laws of DFT operation, and thus quickly developed and improved a set of high-speed and effective operation methods, which is now commonly known as the fast Fourier transform FF11 algorithm. Specifically, the position of a particle and its momentum cannot be determined simultaneously in a quantum mechanical system. It focuses on the proof and application of the Heisenberg inequality by TTF. Due to the different ways and methods of practical application, the practical significance and practical value of the application are for readers' reference. Besides, the space is limited and my knowledge is limited. Finally, the development direction of FFT in quantum physics is summarized.

Optimum DCT type-I based transceiver model and effective channel estimation for uplink NB-IoT system

Single-tone and multi-tone transmissions in the narrowband Internet of Things (NB-IoT) uplink system can be accomplished by employing different orthogonal basis. In this paper, we develop an uplink NB-IoT baseband system model and derive the corresponding analytical signal model based on the discrete cosine transform type-I (DCT-I) domain. Basically, the circular convolution and channel matrix diagonalization issues for designing DCT-based systems are addressed without exploiting any redundancy (a prefix and a suffix sequences, and zero-padding (ZP)) into each transmitted data symbol blocks. In our proposed DCT-I based transceiver, we employ a standard cyclic prefix (CP) and apply discrete Fourier transform (DFT) and inverse DFT (IDFT) operations directly to make the channel matrix circulant and diagonal, resulting in the use of one-tap frequency-domain channel equalizer without incorporating extra front-end prefilter at the receiver. Furthermore, we propose novel least squares (LS) and linear minimum mean square error (LMMSE) channel estimators by considering the energy concentration and spectral compaction properties of DCT-I for the uplink NB-IoT system. The expressions for the DCT-I domain LS and LMMSE estimators are derived for channel frequency response estimation and mean square error computation. Finally, the viability of the proposed CP-DCT-I-NB-IoT uplink system, as well as the channel estimators, are tested compared with the standardized CP-DFT-NB-IoT and ZP-DCT type-2 even based single-carrier frequency-division multiple access (SC-FDMA) systems through rigorous computer simulations.

Systematic Wavelet Codes: Designed and Decoded by DFT Vectors

A class of complex-valued convolutional codes, wavelet codes, that encode numbers into numbers, is constructed by assigning consecutively indexed discrete Fourier transform (DFT) vectors to the parity-checking requirements. For a rate $k/n$ code with constraint length $m$ , the parameters must satisfy (m + 1)(n-k) $m$ , the errors can be corrected by extracting from the convolutional code’s syndromes, new syndromes associated with a DFT block code inherent in the code’s algebraic structure. A modified Berlekamp–Massey algorithm computes the error locations and the correcting values are determined by an inverse DFT operation. Systematic forms of these codes are developed by manipulating the original generating transfer function. Each systematic form is a subcode of the original wavelet code from which it was determined. Moreover, this form may be decoded by DFT code methods too. Extensive simulation results verify the power and viability of both forms of the codes and their decoding techniques.

OTFS(Orthogonal Time Frequency Space) 변조를 사용하는 MIMO(Multiple Input Multiple Output) 시스템 설계와 성능 평가

In this paper, we have evaluated and analyzed OTFS(Orthogonal Time Frequency Space) modulation and OTFS-MIMO(Multiple Input Multiple Output) system. OTFS modulation can concisely compensate delay-Doppler spreading effect by using 2D(2-Dimension) iDFT (inverse Discrete Fourier Transform) and DFT(Discrete Fourier Transform) operation. It enables OTFS system to transmit high-speed data. Especially, OTFS-MIMO system can transmit all data streams without performance degradation on high Doppler frequency channel. As simulation results, we have confirmed that 1×1 OTFS system’s achievable rate is a similar to each stream of 2×2 OTFS-MIMO system. That is, we have also confirmed that 2×2 MIMO system can completely achieve double achievable rate in comparison with OTFS system on high Doppler frequency channel.

AutoNFT: Architecture synthesis for hardware DFT of length-of-coprime-number products

Discrete Fourier Transform (DFT) is widely used in almost all fields of science and engineering. Meanwhile, modern applications processing big data, such as images and sound, require increasingly complex features, such as the long and non-power-of-two hardware DFT and floating-point operations with wide ranges and high effective resolutions. In this paper, we propose a method to extend the matrix-factorization-based DFT algorithm for performing non-power-of-two DFTs of length N equal to the product of coprime numbers. Based on this algorithm, we also present a new DFT architecture synthesizer with high portability, called AutoNFT, to generate hardware DFT in a fully parallel structure. The architecture also contains a high-performance floating-point core to work at 1GHz. DFTs generated by AutoNFT can run at 500 Mhz using a 40nm industry library. This technology can handle 115 billion fixed-point samples per second on 256-point DFT and 13.5 billion floating-point samples per second on 30-point DFT.

Low-complexity linewidth-tolerant time domain sub-symbol optical phase noise suppression in CO-OFDM systems.

Two linewidth-tolerant optical phase noise suppression algorithms, non-decision aided sub-symbol optical phase noise suppression (NDA-SPS) and partial-decision aided sub-symbol optical phase noise suppression (PDA-SPS), based on low-complexity time domain sub-symbol processing are proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. High accuracy carrier phase estimation is achieved in the NDA-SPS algorithm without decision error propagation. Compared with NDA-SPS, partial-decision aided estimation is introduced in PDA-SPS to reduce the pilot-overhead by half, yet only a small performance degradation is induced. The principles and computational complexities of the proposed algorithms are theoretically analyzed. By adopting specially designed comb-type pilot subcarriers, multiplier-free observation-based matrix generation is realized in the proposed algorithms. Computationally intensive discrete Fourier transform (DFT) or inverse DFT (IDFT) operations, which are usually carried out in other high-performance inter-carrier-interference (ICI) mitigation algorithms multiple times, are completely avoided. Compared with several other sub-symbol algorithms, the proposed algorithms with lower complexities offer considerably larger laser linewidth tolerances as demonstrated by Monte-Carlo simulations. Numerical analysis verifies that the optimal performance of PDA-SPS can be achieved with moderate numbers of sub-symbols.

Spectrum analysis of complicated radiolocation signal with binary phase manipulation by Kasami sequence

Introduction. This article contain short introduction to history of complicated signals and list of common sequences, used in spectrum spreading. Method of creating Kasami sequences. In this article is shown sequence creation method, based on method of creating maximum length sequence. Creating of the structural schema of Kasami sequences generator. Principles of construction of Kasami sequence generator are shown in this article. Example of generator for sequence with length 63 symbols, which are created using method, mentioned in previous article, is also shown. Spectrum of Kasami sequences. This article contain amplitude and phase spectrum of two Kasami sequences with lengths of 1023 and 255 symbols. Theoretical formulas are created using Discrete Fourier Transform operation, and graphics are plotted using Fast Fourier Transform operation. Phase spectrum data are also been changed by unwrap operation for better visibility. Conclusion. This article contain analysis of characteristics of previously shown spectrum. Several conclusions are made about correlation between sequence and spectrum characteristics. These conclusions include that made about amplitude spectrum form dependence of sequence length, type and basic impulse characteristics.

Accurate Estimation of Single-Phase Grid Voltage Parameters Under Distorted Conditions

This paper presents an accurate technique for the estimation of single-phase grid voltage fundamental amplitude and frequency. The technique consists of a quadrature signal generator (QSG) and a discrete Fourier transform (DFT). The frequency information required by the QSG based on a second-order generalized integrator (SOGI) is estimated using the spectral leakage property of the DFT. The presented DFT operation does not require real-time evaluation of trigonometric functions. The frequency estimation is less affected by the presence of harmonics when compared to similar techniques based on QSG-SOGI such as the phase-locked loop and the frequency-locked loop. Moreover, unlike these techniques, the DFT-based QSG-SOGI (DFT-SOGI) technique does not create any interdependent loops, thus increasing the overall stability and easing the tuning process. The effectiveness of the proposed technique has been validated on a real-time experimental setup.

Periodic steady state solution of distribution networks via sweeping iterations

This study describes an enhanced hybrid method for calculating the periodic steady state of radial and weakly meshed distribution networks. The forward/backward sweeping technique has been taken here as basis to compute the network's equilibrium, accounting that non-linear elements and electronic devices are included. On one hand, a modified harmonic domain (MHD), based on the discrete Fourier transform (DFT), has been used to account for harmonics and interharmonics simultaneously, involving only matrix/vector operations. On the other hand, non-linear elements and electronic devices are handled in the time domain and included in the sweeping solution scheme by interfacing MHD and time domain through DFT operations. The proposed hybrid sweeping-based technique and a Newton-based method are compared here through a network example.

Efficient receiver algorithms for DFT-spread OFDM systems

For the 3GPP LTE uplink transmissions, the DFTspread OFDM technique has been adopted as the air interface in order to reduce the peak-to-average-power ratio (PAPR). In this scheme, each data symbol is spread over many tones by a discrete Fourier transform (DFT) operation at the transmitter before being sent to the orthogonal frequency division multiplexing (OFDM) modulator. Moreover, more than one user can be scheduled over the same frequency and time resource block (RB) via space-division multiple-access (SDMA). The conventional receiver technique for such DFT-spread OFDM systems involves tone-by-tone single-tap equalization followed by an inverse DFT operation. In this paper, we propose a more powerful receiver technique for DFT-spread OFDM systems that consists of an efficient linear pre-filter and a two-symbol soft output demodulator. The proposed method can be applied to both single-user per RB (DFT-S-OFDMA) and multiple users per RB (DFT-S-OFDMSDMA) systems and it offers significant performance gains over the conventional method, especially in the high-rate regime, with little attendant increase in computational complexity.

Tone interference suppression in DS-SS systems with modified DFT

The performance of traditional interference excision methods based on the discrete Fourier transform (DFT) in direct sequence spread spectrum (DS-SS) systems varies significantly with the frequency of the interference because the DFT of the interference becomes more dispersive with the increase of grid biases in the DFT operation. This paper presents a new excision method using modified DFT (MDFT) with an estimated grid bias. Minimum dispersion of the interference is achieved in the MDFT domain. Both theoretical analysis and experimental simulation are presented to show that the interference can be excised with a minimum distortion of the desired signal in a large range of interference-to-signal ratio.

Performance Evaluation of Quantization Effects on Multicarrier Modulated Signals

The numerical accuracy in the discrete Fourier transform (DFT)/inverse DFT operations can have a significant impact on multicarrier (MC) modulated signals. This accuracy can be modeled by including appropriate quantization devices in the transmission chain. In this paper, we present an analytical approach for analyzing the impact of the quantization effects on MC signals. For this purpose, we statistically characterize the signal along the transmission chain, taking advantage of the Gaussian behavior of MC signals with a high number of subcarriers and employing well-known results on Gaussian signals and memoryless nonlinearities. This statistical characterization can then be used for performance evaluation of given quantization characteristics, in a simple and computationally efficient way, as well as for its optimization.

Preliminary Field Results on a New Transient Induction System Employing Pseudo-Noise Signals

An experimental system is described which utilizes pseudo-noise (PN) and cross-correlation techniques to characterize subsurface conducting bodies such as those pertaining to natural resources. The system is essentially an extension of the loop-loop, transient-electromagnetic, induction systems used in ore prospecting. In lieu of a low duty-cycle pulse, this system transmits a wide-bandwidth PN digital waveform. The mapping signature is obtained by cross-correlation of the received signal with a replica of the sounding PN waveform. The receiver also averages several signatures to improve the signal-to-noise ratio. This type of system has the potential advantages over previous transient systems of using smaller antennas and requiring less transmitter power for more portable operation. Preliminary field data is shown and discussed for a high conductivity dike of ilmenite magnetite and for the surrounding low conductivity anorthosite. Frequency response data is obtained digitally via the Discrete Fourier Transform operation on the time domain signatures. Interpretations are given for both time and frequency domain representations.