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What are some practical applications of the Fourier Transform in signal processing?

Discrete Fourier transform

Conjugate Fourier series

Fourier inversion theorem

Discrete Fourier series

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The Fourier Transform finds practical applications in various signal processing domains. In Digital Signal Processing (DSP), it aids in analyzing and enhancing signals like audio music by breaking them down into frequency components . Additionally, the Fourier Transform is crucial in fields like mobile telephony, mobile internet, and automatic control in modern appliances and transport systems, motivating readers to grasp its basics . Moreover, it plays a significant role in minimizing hardware costs for implementing frequency selection algorithms on programmable logic devices without multiplication operations, through the multi-stage discrete Fourier transform methodology . Furthermore, in biomedical signal processing, Fourier Transform is utilized alongside Wavelet Transform to process low-frequency signals like ECG and PPG for accurate clinical monitoring and diagnosis .

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Open access•Book Chapter•DOI Use of Transforms in Biomedical Signal Processing and Analysis Ette Harikrishna, Komalla Ashoka Reddy - Show less +1 more 29 May 2021 2 Citations	The Fourier Transform is used in signal processing for tasks like reducing motion artifacts in biomedical signals, generating reference signals for adaptive filters, and analyzing stationary signals effectively.
Open access•Journal Article•DOI Applications of Fourier series and Fourier Transform in Electrical and Electronics Devices Prof. S. M. Shende, D. G. Lanjewar - Show less +1 more 30 Apr 2023-International Journal For Science Technology And Engineering	The Fourier Transform is utilized in signal processing for frequency response analysis of filters, solving PDEs, Discrete Fourier Transform, FFT in signal analysis, and digital multimedia visualization systems.
Open access•DOI An application of Fourier transform through Matlab in classifying tempos Nur Asifa Mohd Ali, Hajar Sulaiman - Show less +1 more 18 Nov 2021	The Fourier Transform is utilized in signal processing, like in this study, to convert time-domain signals into frequency-domain signals, aiding in tasks such as classifying tempos in audio music.
Open access•Book Chapter•DOI Introduction 01 Jan 2022	The Fourier Transform is crucial in signal processing applications like mobile telephony, mobile Internet, automatic control in household appliances, and LTE signal reception, making modern technologies reliant on it.
Proceedings Article•DOI Digital Signal Multi-Stage Discrete Fourier Transform and Its Practical Applications Adeliya Yu. Burova 24 Mar 2021 9 Citations	The practical applications of the Fourier Transform in signal processing include minimizing hardware costs for frequency selection of digital signals on programmable logic devices using multi-stage discrete Fourier transform without multiplication operations.

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What are the advantages and limitations of using the Fourier transform technique for signal analysis in wheel-rail systems?4 answersThe Fourier transform technique has limitations when used for signal analysis in wheel-rail systems. It struggles with nonstationary and nonlinear signals, which are common in these systems. Additionally, the Fourier transform does not provide detailed insights into defect type and severity, limiting its usefulness in wheel condition monitoring. However, the Fourier transform does have advantages. It is a widely used method for time-frequency analysis and can provide frequency information about the signals. It can also be used to analyze the power spectral density of vibration signals, which can be correlated with wheel flat and von Mises stress in wheel-rail systems. Overall, while the Fourier transform has limitations in dealing with nonstationary and nonlinear signals and providing detailed defect information, it can still be useful for frequency analysis and correlation studies in wheel-rail systems.

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How the fourier transform work in signal processing?5 answersThe Fourier transform is a method used in signal processing to analyze and convert signals. It allows us to analyze both digital and continuous signals, depending on the specific needs of the problem. The Fourier transform works by decomposing a signal into its frequency components using a continuum of continuous sinusoids over an infinite frequency range. This analysis can be used to compute the system response, modulate waves for communication, and perform other applications. In signal processing, the Fourier transform can be implemented using methods such as the discrete Fourier transform (DFT) and the fast Fourier transform (FFT). These methods involve converting the signal into a digital format, filtering it, and then applying the Fourier transform to obtain the frequency components of the signal. The Fourier transform is a powerful tool in signal processing that allows for the analysis and manipulation of signals in both the time and frequency domains.

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