Higher Engineering Mathematics, Sixth Edition
622 Higher Engineering Mathematics in the range 0 to 2π. y 0 21 1 2 Figure 67.5 Sketch the waveform defined by: f(x)= ⎧ ...
Chapter 68 Even and odd functions and half-range Fourier series 68.1 Even and odd functions Even functions A functiony=f(x)is sa ...
624 Higher Engineering Mathematics Problem 1. Determine the Fourier series for the periodic function defined by: f(x)= ⎧ ⎪⎪ ⎪⎪ ⎪ ...
Even and odd functions and half-range Fourier series 625 2 f(x) (^0) x 22 2 2 3 Figure 68.2 The square wave shown in Fig. ...
626 Higher Engineering Mathematics Hence the Fourier series is: f(θ)=θ^2 = π^2 3 − 4 ( cosθ− 1 22 cos2θ+ 1 32 cos3θ − 1 42 cos 4 ...
Even and odd functions and half-range Fourier series 627 22 ^02 A x B f(x) f(x) 5 x 2 Figure 68.4 (b) If ahalf-range cos ...
628 Higher Engineering Mathematics Problem 7. Find the half-range Fourier sine series to represent the functionf(x)= 3 xin the r ...
Even and odd functions and half-range Fourier series 629 Hence the half-range Fourier sine series forf(x)in the range 0 toπis gi ...
Chapter 69 Fourier series over any range 69.1 Expansion of a periodicfunction of periodL (a) A periodic function f(x) of period ...
Fourier series over any range 631 Period L 58 ms 0 10 v (t) (^28244812) t (ms) Figure 69.1 The square wave is shown in Fig. 69.1 ...
632 Higher Engineering Mathematics Thus, from para. (c), f(x)=a 0 + ∑∞ n= 1 ancos ( 2 πnx L ) a 0 = 1 L ∫ L 2 −L 2 f(x)dx= 1 4 ∫ ...
Fourier series over any range 633 = 2 3 ⎡ ⎢ ⎢ ⎢ ⎣ tsin ( 2 πnt 3 ) ( 2 πn 3 ) + cos ( 2 πnt 3 ) ( 2 πn 3 ) 2 ⎤ ⎥ ⎥ ⎥ ⎦ 3 0 by pa ...
634 Higher Engineering Mathematics Determine the Fourier series for the half wave rectified sinusoidal voltage Vsinωt defined b ...
Fourier series over any range 635 Whennis even,an= 0 a 1 = − 8 π^2 , a 3 = − 8 π^232 , a 5 = − 8 π^252 and so on. Hence the half ...
636 Higher Engineering Mathematics Determine the half-range Fourier sine series for the function defined by: f(t)= { t, 0 < ...
Chapter 70 A numerical method of harmonic analysis 70.1 Introduction Many practical waveforms can be represented by sim- ple mat ...
638 Higher Engineering Mathematics interval is thus 2 π p . Let the ordinates be labelledy 0 , y 1 ,y 2 ,...yp(note thaty 0 =yp) ...
A numerical method of harmonic analysis 639 Table 70.1 Ordin- ates θ◦ V cosθ Vcosθ sinθ Vsinθ cos2θ Vcos2θ sin2θ Vsin2θ cos3θ Vc ...
640 Higher Engineering Mathematics b 2 ≈ 2 12 ( 29. 43 )= 4. 91 and b 3 ≈ 2 12 ( 55 )= 9. 17 Substituting these values into the ...
A numerical method of harmonic analysis 641 70.3 Complex waveform considerations It is sometimes possible to predict the harmoni ...
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