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Using Fourier Analysis -which is too difficult to explain in this forum.
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
Spectral analysis of a repetitive waveform into a harmonic series can be done by Fourier analyis. This idea is generalised in the Fourier transform which converts any function of time expressed as a into a transform function of frequency. The time function is generally real while the transform function, also known as a the spectrum, is generally complex. A function and its Fourier transform are known as a Fourier transform pair, and the original function is the inverse transform of the spectrum.
Discrete fourier coefficients are the samples of fourier transform of the non-pdc waveform, at pdc intervals
Fourier analysis Frequency-domain graphs
Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis. Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation. If you want to find out more, look up fourier synthesis and the fourier transform.
The main advantage of using sinusoidal waveform is that any waveform can be represented using a sinusoidal wave (by applying Fourier series). Also, analysing a circuit (or any other system) becomes simpler and easier using sinusoidal signal as test signal.
Tatsuo Kawata has written: 'Fourier analysis in probability theory' -- subject(s): Fourier series, Fourier transformations, Probabilities
Randall J. LeVeque has written: 'Fourier analysis of the SOR iteration' -- subject- s -: Iterative solution, SOR iteration, Fourier analysis
B. T. Grothaus has written: 'Fourier grain shape analysis' -- subject(s): Alluvial fans, Fourier analysis, Correlation (Statistics)
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
The general field of Fourier analysis is often known as harmonic analysis. The Fourier analysis it occurs in the modeling time-dependent phenomena such as speech, EKGs, EEGs, earthquakes and tides. Examples also include the study of vibrations and circular, physical and rectangular pictures. It also involves the transmission of pictures including the weather or pictures of remote planets taken by space probes.