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Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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Aliasing01:18

Aliasing

189
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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Sampling Theorem01:15

Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

121
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Functional Near-Infrared Spectroscopy Hyperscanning Study in Psychological Counseling
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Estimation of a Spectral Correlation Function Using a Time-Smoothing Cyclic Periodogram and FFT Interpolation-2N-FFT

Timofey Shevgunov1, Evgeny Efimov1, Oksana Guschina1

  • 1Moscow Aviation Institute, Volokolamskoe Shosse 4, 125993 Moscow, Russia.

Sensors (Basel, Switzerland)
|January 8, 2023
PubMed
Summary

This study introduces a novel double-number fast Fourier transform (2N-FFT) algorithm for accurate spectral correlation function (SCF) estimation. The 2N-FFT algorithm improves the characterization of cyclostationary properties in random processes and signals.

Keywords:
cyclic spectrumcyclostationaritycyclostationary random processfast Fourier transform (FFT)spectral correlation analysisspectral correlation densityspectral correlation functionspectrum estimation

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Area of Science:

  • Signal Processing
  • Statistical Signal Analysis
  • Time Series Analysis

Background:

  • Wide-sense cyclostationary processes are fundamental models for time series and discrete-time signals.
  • Accurate estimation of the spectral correlation function (SCF) is crucial for characterizing these processes.
  • Existing methods may have limitations in resolution cell coverage and computational efficiency.

Purpose of the Study:

  • To propose and describe a novel digital signal processing technique for estimating the spectral correlation function (SCF).
  • To address limitations in existing SCF estimation methods, particularly regarding resolution cell coverage in the bifrequency plane.
  • To introduce the double-number fast Fourier transform (2N-FFT) algorithm for enhanced SCF estimation.

Main Methods:

  • Development of the double-number fast Fourier transform (2N-FFT) algorithm.
  • Derivation of the 2N-FFT from a time-smoothing approach to cyclic periodogram estimation.
  • Application of spectral interpolation by doubling the Fast Fourier Transform (FFT) base.
  • Numerical simulations using modulated processes to validate the algorithm.

Main Results:

  • The 2N-FFT algorithm ensures complete coverage of cyclic frequencies without gaps.
  • Numerical simulations demonstrated high accuracy in estimating cyclic frequencies for complex signal models.
  • Estimated SCF components closely matched theoretical models, validating the algorithm's performance.
  • The 2N-FFT algorithm offers a favorable trade-off in computational complexity and memory requirements compared to the FFT accumulation method.

Conclusions:

  • The proposed 2N-FFT algorithm provides an accurate and efficient method for spectral correlation function estimation.
  • This technique enhances the quantitative characterization of wide-sense cyclostationary properties in signals.
  • The 2N-FFT algorithm presents a valuable alternative for digital signal processing applications requiring precise SCF analysis.