This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a ...This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.展开更多
To address the problem that it is difficult to detect an intermediate frequency(IF)signal at the receiving end of a communication system under extremely low signal-to-noise ratio(SNR)conditions,we propose a stochastic...To address the problem that it is difficult to detect an intermediate frequency(IF)signal at the receiving end of a communication system under extremely low signal-to-noise ratio(SNR)conditions,we propose a stochastic resonance(SR)-enhanced sine-signal detection method based on the sign function.By analyzing the SR mechanism of the sine signal and combining it with the characteristics of a dual-sequence frequency-hopping(DSFH)receiver,a periodic stationary solution of the Fokker-Planck equation(FPE)with a time parameter is obtained.The extreme point of the sine signal is selected as the decision time,and the force law of the electromagnetic particles is analyzed.A receiving structure based on the sign function is proposed to maximize the output difference of the system,and the value condition of the sign function is determined.In order to further improve the detection performance,in combination with the central-limit theorem,the sampling points are averaged N times,and the signal-detection problem is transformed into a hypothesis-testing problem under a Gaussian distribution.The theoretical analysis and simulation experiment results confirm that when N is 100 and the SNR is greater than 20 dB,the bit-error ratio(BER)is less than 1.5×10^(-2) under conditions in which the signal conforms to the optimal SR parameters.展开更多
文摘This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.
基金Project supported by the Natural Science Foundation of Hebei Province of China(Grant Nos.F2019506031,F2019506037,and F2020506036)the Frontier Innovation Program of Army Engineering University(Grant No.KYSZJQZL2005)the Basic Frontier Science and Technology Innovation Program of Army Engineering University(Grant No.KYSZJQZL2020).
文摘To address the problem that it is difficult to detect an intermediate frequency(IF)signal at the receiving end of a communication system under extremely low signal-to-noise ratio(SNR)conditions,we propose a stochastic resonance(SR)-enhanced sine-signal detection method based on the sign function.By analyzing the SR mechanism of the sine signal and combining it with the characteristics of a dual-sequence frequency-hopping(DSFH)receiver,a periodic stationary solution of the Fokker-Planck equation(FPE)with a time parameter is obtained.The extreme point of the sine signal is selected as the decision time,and the force law of the electromagnetic particles is analyzed.A receiving structure based on the sign function is proposed to maximize the output difference of the system,and the value condition of the sign function is determined.In order to further improve the detection performance,in combination with the central-limit theorem,the sampling points are averaged N times,and the signal-detection problem is transformed into a hypothesis-testing problem under a Gaussian distribution.The theoretical analysis and simulation experiment results confirm that when N is 100 and the SNR is greater than 20 dB,the bit-error ratio(BER)is less than 1.5×10^(-2) under conditions in which the signal conforms to the optimal SR parameters.
