[한양대 기계공학부] 동역학제어실험 실험1 진동 신호의 시간 및 주파수 영역 해석 A+ 자료

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1. Fourier Series

Fourier Series는 모든 주기 함수를 일련의 sine, cosine 함수들의 합으로 나타낼 수 있다는 것을 설명합니다. 이를 통해 시간 영역에서의 신호가 주파수 영역에서는 어떻게 해석되는지 이해할 수 있습니다.
2. Fourier Integral

Fourier Integral은 Fourier Series에서 주기가 점점 길어져 무한대로 늘어나게 되면 주파수 영역에서 주파수간의 간격이 점점 좁아지다가 극한에 이르러 연속함수가 된다는 것을 설명합니다.
3. Fourier Transform

Fourier Transform은 시간 영역의 신호를 주파수 영역으로 변환하는 방법을 설명합니다. 이를 통해 시간 영역에서의 신호가 주파수 영역에서 어떻게 나타나는지 확인할 수 있습니다.
4. MATLAB의 FFT 사용

MATLAB의 FFT(Fast Fourier Transform) 기능을 이용하여 시간 영역의 신호를 주파수 영역으로 변환하는 방법을 설명합니다.
5. Sine wave 분석

Sine wave 입력 신호를 시간 영역과 주파수 영역에서 분석하고, 이론적인 예측과 실험 결과를 비교합니다.
6. Square wave 분석

Square wave 입력 신호를 시간 영역과 주파수 영역에서 분석하고, 이론적인 예측과 실험 결과를 비교합니다. Square wave의 경우 기함수 특성으로 인해 주파수 영역에서 특정 주파수 성분만 나타나는 것을 확인할 수 있습니다.

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1. Fourier Series

Fourier Series is a powerful mathematical tool that allows us to represent periodic functions as the sum of sine and cosine waves. It has wide applications in various fields, including signal processing, electrical engineering, and physics. The ability to decompose a complex waveform into its fundamental frequency components provides valuable insights and enables us to analyze and manipulate signals more effectively. Fourier Series is a fundamental concept that lays the foundation for understanding more advanced topics like Fourier Transforms and their applications.
2. Fourier Integral

The Fourier Integral is an extension of the Fourier Series, allowing us to represent non-periodic functions as a continuous spectrum of frequency components. This is particularly useful for analyzing and processing aperiodic signals, such as transient or non-repeating waveforms. The Fourier Integral provides a mathematical framework for understanding the frequency domain representation of these signals, which is crucial in areas like signal processing, communication systems, and image processing. Understanding the Fourier Integral and its properties is essential for gaining a deeper understanding of the Fourier Transform and its applications.
3. Fourier Transform

The Fourier Transform is a fundamental mathematical tool that allows us to analyze and manipulate signals in the frequency domain. It provides a powerful way to decompose a signal into its constituent frequency components, enabling us to gain valuable insights and perform various signal processing tasks. The Fourier Transform has widespread applications in fields such as communications, signal processing, image processing, and quantum mechanics. Understanding the properties and applications of the Fourier Transform is crucial for anyone working with signals and systems, as it provides a deeper understanding of the underlying principles and enables more effective analysis and processing of complex waveforms.
4. Sine wave analysis

Sine waves are fundamental building blocks of many signals and waveforms, and their analysis is crucial in various fields, including electrical engineering, signal processing, and physics. Understanding the properties of sine waves, such as their frequency, amplitude, and phase, is essential for analyzing and manipulating complex signals. Sine wave analysis provides insights into the underlying frequency components of a signal, enabling the application of Fourier-based techniques for signal processing, filtering, and spectral analysis. Mastering the analysis of sine waves is a crucial step in developing a deeper understanding of signal theory and its practical applications.