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What is Fourier series?
- a)The representation of periodic signals in a mathematical manner is called a Fourier series
- b)The representation of non periodic signals in a mathematical manner is called a Fourier series
- c)The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier series
- d)The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier series
Correct answer is option 'D'. Can you explain this answer?
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What is Fourier series?a)The representation of periodic signals in a m...
The Fourier series is the representation of non periodic signals in terms of complex exponentials, or equivalently in terms of sine and cosine waveform leads to Fourier series. In other words, Fourier series is a mathematical tool that allows representation of any periodic wave as a sum of harmonically related sinusoids.
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What is Fourier series?a)The representation of periodic signals in a m...
Fourier series:
The Fourier series is a mathematical representation of periodic signals in terms of complex exponentials or sinusoids. It was developed by Jean-Baptiste Joseph Fourier, a French mathematician, in the early 19th century. The series allows us to decompose a periodic signal into a sum of sine and cosine functions with different frequencies and amplitudes.
Representation of periodic signals:
The Fourier series is specifically designed to represent periodic signals. A periodic signal is one that repeats itself over time, such as a sine wave or a square wave. By using the Fourier series, we can express any periodic signal as an infinite summation of sinusoidal functions.
Complex exponentials and sinusoids:
The Fourier series can be expressed in terms of either complex exponentials or sinusoids. A complex exponential is a function of the form e^(iωt), where i is the imaginary unit (√-1), ω is the angular frequency, and t is time. A sinusoid is a function of the form A*sin(ωt) or A*cos(ωt), where A is the amplitude of the signal.
Fourier series coefficients:
The Fourier series representation of a periodic signal consists of a series of coefficients multiplied by the complex exponentials or sinusoids. These coefficients determine the amplitude and phase of each component in the signal. The coefficients can be calculated using Fourier series formulas or by integrating the signal with respect to time.
Applications:
The Fourier series has numerous applications in various fields, including engineering, physics, and signal processing. It is used to analyze and manipulate signals in the frequency domain, allowing us to extract valuable information about the signal's frequency content. Fourier series also forms the basis for more advanced techniques such as Fourier transform and spectral analysis.
Conclusion:
In conclusion, the Fourier series is a powerful mathematical tool for representing periodic signals in terms of complex exponentials or sinusoids. It provides a way to decompose a periodic signal into its frequency components and determine their amplitudes and phases. This representation has wide-ranging applications in various fields and is fundamental to the study of signals and systems.
The Fourier series is a mathematical representation of periodic signals in terms of complex exponentials or sinusoids. It was developed by Jean-Baptiste Joseph Fourier, a French mathematician, in the early 19th century. The series allows us to decompose a periodic signal into a sum of sine and cosine functions with different frequencies and amplitudes.
Representation of periodic signals:
The Fourier series is specifically designed to represent periodic signals. A periodic signal is one that repeats itself over time, such as a sine wave or a square wave. By using the Fourier series, we can express any periodic signal as an infinite summation of sinusoidal functions.
Complex exponentials and sinusoids:
The Fourier series can be expressed in terms of either complex exponentials or sinusoids. A complex exponential is a function of the form e^(iωt), where i is the imaginary unit (√-1), ω is the angular frequency, and t is time. A sinusoid is a function of the form A*sin(ωt) or A*cos(ωt), where A is the amplitude of the signal.
Fourier series coefficients:
The Fourier series representation of a periodic signal consists of a series of coefficients multiplied by the complex exponentials or sinusoids. These coefficients determine the amplitude and phase of each component in the signal. The coefficients can be calculated using Fourier series formulas or by integrating the signal with respect to time.
Applications:
The Fourier series has numerous applications in various fields, including engineering, physics, and signal processing. It is used to analyze and manipulate signals in the frequency domain, allowing us to extract valuable information about the signal's frequency content. Fourier series also forms the basis for more advanced techniques such as Fourier transform and spectral analysis.
Conclusion:
In conclusion, the Fourier series is a powerful mathematical tool for representing periodic signals in terms of complex exponentials or sinusoids. It provides a way to decompose a periodic signal into its frequency components and determine their amplitudes and phases. This representation has wide-ranging applications in various fields and is fundamental to the study of signals and systems.
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What is Fourier series?a)The representation of periodic signals in a mathematical manner is called a Fourier seriesb)The representation of non periodic signals in a mathematical manner is called a Fourier seriesc)The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesd)The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesCorrect answer is option 'D'. Can you explain this answer?
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What is Fourier series?a)The representation of periodic signals in a mathematical manner is called a Fourier seriesb)The representation of non periodic signals in a mathematical manner is called a Fourier seriesc)The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesd)The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesCorrect answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What is Fourier series?a)The representation of periodic signals in a mathematical manner is called a Fourier seriesb)The representation of non periodic signals in a mathematical manner is called a Fourier seriesc)The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesd)The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is Fourier series?a)The representation of periodic signals in a mathematical manner is called a Fourier seriesb)The representation of non periodic signals in a mathematical manner is called a Fourier seriesc)The representation of non periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesd)The representation of periodic signals in terms of complex exponentials or sinusoids is called a Fourier seriesCorrect answer is option 'D'. Can you explain this answer?.
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