Sinopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...different curves might result from adding together three sine-curves. The curve shown in figure 30, is the resultant of three sinecurves, having 1, 3 and 5 times the frequency of the resultant, and having maxima values of 3, 2 and 1 respectively, relative to the component sinecurve having 5 times the frequency of the resultant; designated in the figure as the 5th harmonic. If the three sine-curves had had maxima values in the rtrerse order given; namely, 1st, 1; 2nd, 2, and 3rd, 3, and the three curves added, a very different resultant curve would have been found. It is thus seen that a large variety of shapes may be found for the resultant curve, by simply varying magnitudes. Greater variations result from varying frequencies and relative position of the component sine-eurves. Fourier, in investigating this fact discovered that a certain number of sine-curves of different frequencies, maxima values, and phase position may be found and added together to form the given irregular periodic, or alternating-curve, and formulated a systematic method for finding the numerical values of the frequencies and maxima values of the component sine-curves. The method of finding the component sine-curves that unite to form any given irregular alternating-curve, is what may be called the analysis of the given curve. This process is exactly the reverse of the process of adding together a given number of definite sine-curves to form a resultant periodic curve. The latter process is "synthesis", and is a much simpler operation than that of analyzing a given curve to evaluate its proper sinecomponents. Many important facts may however be ascertained by the graphical process of constructing alternating-curves from given sine-curves; either by adding sine-curves togethe...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1916 Excerpt: ...different curves might result from adding together three sine-curves. The curve shown in figure 30, is the resultant of three sinecurves, having 1, 3 and 5 times the frequency of the resultant, and having maxima values of 3, 2 and 1 respectively, relative to the component sinecurve having 5 times the frequency of the resultant; designated in the figure as the 5th harmonic. If the three sine-curves had had maxima values in the rtrerse order given; namely, 1st, 1; 2nd, 2, and 3rd, 3, and the three curves added, a very different resultant curve would have been found. It is thus seen that a large variety of shapes may be found for the resultant curve, by simply varying magnitudes. Greater variations result from varying frequencies and relative position of the component sine-eurves. Fourier, in investigating this fact discovered that a certain number of sine-curves of different frequencies, maxima values, and phase position may be found and added together to form the given irregular periodic, or alternating-curve, and formulated a systematic method for finding the numerical values of the frequencies and maxima values of the component sine-curves. The method of finding the component sine-curves that unite to form any given irregular alternating-curve, is what may be called the analysis of the given curve. This process is exactly the reverse of the process of adding together a given number of definite sine-curves to form a resultant periodic curve. The latter process is "synthesis", and is a much simpler operation than that of analyzing a given curve to evaluate its proper sinecomponents. Many important facts may however be ascertained by the graphical process of constructing alternating-curves from given sine-curves; either by adding sine-curves togethe...
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