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Discrete-time Fourier transform01:26

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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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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.
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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.
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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.
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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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Discrete Fourier Transform with Denoise Model Based Least Square Wiener Channel Estimator for Channel Estimation in

Dhanasekaran S1, SatheeshKumar Palanisamy2, Fahima Hajjej3

  • 1Department of E.C.E., Sri Eshwar College of Engineering, Coimbatore 641202, India.

Entropy (Basel, Switzerland)
|November 11, 2022
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Summary

This study introduces an Improved Channel Estimation Algorithm (ICEA-DA) using DFT-LS-WIENER for efficient Multiple-Input Multiple-Output (MIMO) systems. The new method significantly improves bit error rate (BER) performance in multipath environments.

Keywords:
MIMOOFDMchannel estimationdiscrete Fourier transformleast square estimatorminimum mean square error

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Area of Science:

  • Wireless Communication
  • Signal Processing
  • Information Theory

Background:

  • Multiple-Input Multiple-Output (MIMO) systems rely on Orthogonal Frequency Division Multiplexing (OFDM) for efficient multipath communication.
  • Accurate Channel Estimation (C.E.) is crucial for time-varying channel conditions in wireless systems.
  • Existing C.E. techniques often suffer from complexity and suboptimal performance.

Purpose of the Study:

  • To develop a simplified and more accurate channel estimation algorithm for MIMO-OFDM systems.
  • To address the complexity and performance limitations of conventional C.E. methods.
  • To enhance the reliability and efficiency of wireless signal reception.

Main Methods:

  • Developed an Improved Channel Estimation Algorithm integrated with DFT-LS-WIENER (ICEA-DA).
  • Employed Discrete Fourier Transform (DFT) with Least Squares (LS) and Wiener filtering for channel estimation.
  • Utilized Quadrature Phase Shift Keying (QPSK) modulation and pulse modeling at the transmitter.

Main Results:

  • The proposed DFT-LS-WIENER method demonstrates superior performance over LS, LS-DFT, MMSE, and MMSE-DFT.
  • Significant reductions in Bit Error Rate (BER) were observed, e.g., 48.19% at 15 dB SNR compared to LS.
  • Improved metrics include Symbol Error Rate (SER), Channel Capacity (CC), and Peak Signal-to-Noise Ratio (PSNR).

Conclusions:

  • The DFT-LS-WIENER algorithm offers a more precise and efficient solution for channel estimation in MIMO systems.
  • The proposed method effectively reduces complexity while enhancing BER performance.
  • ICEA-DA provides a robust and improved approach compared to traditional channel estimation techniques.