- Published: October 27, 2022
- Updated: October 27, 2022
- Level: Bachelors Degree
- Language: English
- Downloads: 29
Discussion- Paraphrased Fourier series refers to the continuous periodic function that constitutes several cosine and sine waves. In technical terms, the process of computing a Fourier is called harmonic analysis. The analysis helps in solving both ununiformed and arbitrary periodic functions. Solving the graphs is procedural since each graph has to be solved solely before bringing all the results together to evaluate the final solution. The number of harmonics involved in the calculation determines the accuracy of the Fourier series. If less number of harmonics is used, the accuracy of the results decreases.
The term, total squared error, is used in defining the accuracy of the original signal in the Fourier series. The accuracy of the Fourier series can only escalate if the value of “ m” increases. The accuracy, for example, deteriorates or is very low when the value of “ m” is 1. Consequently, the accuracy of the experiment is very high when the “ m” value stands at 6. The poor accuracy results from the failure to take into consideration the original signal. The original signal serves as a crucial first step towards solving the Fourier series. It is, therefore, important to have a high value as “ m” in order to increase the accuracy of the series.
H. Wilbraham was the first scholar to identify the Gibbs phenomenon. Josiah Gibbs then later studied the phenomenon in detail. The phenomenon has a direct relationship with the Fourier series. It appears as a small sinusoidal wave in square waves. The phenomenon forms part of the troughs and peaks in the series. The sinusoidal waves cannot be eliminated unless the “ m” rises to infinity. In other words, the small peaks forming parts of the square waves are always present.
There are several uses of Fourier series in Electrical engineering. There are, for example, very useful in studies involving harmonic analysis. Harmonic analysis refers to the assessment of periodic functions that constitute simple sinusoidal elements. The methods are of immense importance in noise analysis, filter designing, and signal analysis. These are just a few areas of the wide harmonic analysis that calls for thorough understanding before undertaking computations of the analysis.
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