86 THE STUDY OF SPEECH CURVES 



Sir 



k 



fli = - J w. COS ikt.dt ^ 



in 

 J 



k C 

 ^'=-jy.smikt.dt (16) 



^ 



(t^l, 2, 3, . . . ) 

 Equation (12) appears in this form as 



y = C + Ci.sin{kt—qi) + C2.sin{2kt — q2) +C3.sm{3kt~q3) + ... (17) 



To perform a harmonic analysis the wave-length T is divided into a 

 number m of equal parts /i(thus, T=mh), giving along the time-axis the 

 equidistant points U, ti, U, h, . . . tj, . . . t„^i = 0, h, 2h, 3h, . . . 

 jh, . . . (m. — l)h. The ordinates at these points, yo, yi, y^, ya, . . . 

 yj, ■ • • ym-h are then measured. With these finite values {dt = h), the 

 coefficients (8, 9, 10) become 



(18) 



(19) 



(20) 



(21) 



+ . . . +2/„_, ) 



2 



«i=z,(2/o-cosO 4-?/,.cos ^-|-i/2.cos2A + 2/3.cos3/i-F . . . +2/„-i.cos [m — \]h) 



2 



^\ = —{y^-^^^ ^ ^ y^-^^T^ A + t/2-sin 2/1 + t/3.sin 3/i + . . . +2/„_i.sin [m— l];i) 



/ft- 



2, 



02=— (i/o-cosO +?/i.cos2/i-|-y2.cos4/i + 2/3.COS 6/i+ . . . +w„_i.cos2[w— llA) 

 w 



