Expression 5: "X" left parenthesis, "t" , right parenthesis equals left parenthesis, 1 minus cos left parenthesis, StartFraction, pi "k" Over 2 , EndFraction , right parenthesis , right parenthesis left parenthesis, 1 minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 25 , EndAbsoluteValue Over StartAbsoluteValue, "t" , EndAbsoluteValue minus 25 , EndFraction , right parenthesis StartFraction, StartAbsoluteValue, "t" , EndAbsoluteValue Over "t" , EndFraction left parenthesis, 1.5sin left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 1 , EndAbsoluteValue , right parenthesis , right parenthesis plus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 4 , EndAbsoluteValue plus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 6 , EndAbsoluteValue minus 3 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 7 , EndAbsoluteValue minus 2sin left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 7 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 8 , EndAbsoluteValue minus 15 , right parenthesis , right parenthesis minus 3 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 8 , EndAbsoluteValue plus 3 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 9 , EndAbsoluteValue minus 1.4sin left parenthesis, StartFraction, pi Over 2 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 9 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue plus 3.5 , right parenthesis , right parenthesis plus StartFraction, 2 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue Over left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , right parenthesis , EndFraction minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue plus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue plus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue Over left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , right parenthesis , EndFraction plus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue minus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue minus StartFraction, 8.0 2 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , right parenthesis , EndFraction plus 4cos left parenthesis, StartFraction, pi Over 2 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , EndAbsoluteValue , right parenthesis , right parenthesis plus StartFraction, 3 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , right parenthesis , EndFraction minus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 14 , EndAbsoluteValue plus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , EndAbsoluteValue minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , right parenthesis , EndFraction plus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 17 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 17 , right parenthesis , EndFraction minus .5cos left parenthesis, pi left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 17 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue , right parenthesis , right parenthesis minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue Over left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , right parenthesis , EndFraction plus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue minus 5 quarters StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 19 , EndAbsoluteValue plus 1 quarter StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , EndAbsoluteValue plus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , EndAbsoluteValue Over 4 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , right parenthesis , EndFraction plus .5sin left parenthesis, StartFraction, pi Over 8 , EndFraction left parenthesis, StartAbsoluteValue, "t" minus 21 , EndAbsoluteValue minus StartAbsoluteValue, "t" minus 22 , EndAbsoluteValue plus 4 , right parenthesis , right parenthesis plus 1.2 5 , right parenthesisXt=1−cosπk21−t−25t−25tt1.5sinπ4t−t−1+t−4+12t−6−32t−7−2sinπ4t−7−t−8−15−32t−8+32t−9−1.4sinπ2t−9−t−10+3.5+2t−10t−10−t−10+t−11+t−11t−11+12t−11−12t−12−8.02t−122t−12+4cosπ2t−12−t−13+3t−132t−13−12t−14+12t−15−t−152t−15+t−172t−17−.5cosπt−17−t−18−t−18t−18+t−18−54t−19+14t−21+t−214t−21+.5sinπ8t−21−t−22+4+1.25
5
Expression 6: "Y" left parenthesis, "t" , right parenthesis equals left parenthesis, 1 minus cos left parenthesis, StartFraction, pi "k" Over 2 , EndFraction , right parenthesis , right parenthesis left parenthesis, 1 minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 25 , EndAbsoluteValue Over StartAbsoluteValue, "t" , EndAbsoluteValue minus 25 , EndFraction , right parenthesis sine left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 2 , EndAbsoluteValue , right parenthesis , right parenthesis plus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 2 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 4 , EndAbsoluteValue minus StartFraction, 1 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 4 , EndAbsoluteValue Over 4 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 4 , right parenthesis , EndFraction plus StartFraction, 5 Over 16 , EndFraction left parenthesis, 1 half left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 4 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 6 , EndAbsoluteValue plus 1.2 , right parenthesis , right parenthesis to the 4th power minus 2 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 6 , EndAbsoluteValue plus 2 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 7 , EndAbsoluteValue minus 2sine left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 7 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 8 , EndAbsoluteValue minus 17 , right parenthesis , right parenthesis plus left parenthesis, 1 half left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 8 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 9 , EndAbsoluteValue minus 1 , right parenthesis , right parenthesis squared plus sine left parenthesis, StartFraction, pi Over 2 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 9 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue plus 4 , right parenthesis , right parenthesis plus StartFraction, 4.9 2 4 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , right parenthesis , EndFraction minus 7 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 10 , EndAbsoluteValue plus 7 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue plus StartFraction, 7 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , right parenthesis , EndFraction minus StartFraction, 6.0 0 7 Over 2 , EndFraction StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 11 , EndAbsoluteValue plus StartFraction, 6.0 0 7 Over 2 , EndFraction StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue plus StartFraction, 29 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue Over 16 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , right parenthesis , EndFraction minus 2.5cosine left parenthesis, StartFraction, pi Over 2 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 12 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , EndAbsoluteValue plus 1 , right parenthesis , right parenthesis minus StartFraction, 1 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , right parenthesis , EndFraction plus 3 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 13 , EndAbsoluteValue minus 3 halves StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 14 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 14 , EndAbsoluteValue plus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , EndAbsoluteValue minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , EndAbsoluteValue Over left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 15 , right parenthesis , EndFraction plus .5cosine left parenthesis, pi left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 17 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue , right parenthesis , right parenthesis minus StartFraction, 1 StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue Over 2 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , right parenthesis , EndFraction plus 1 half sine left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 18 , EndAbsoluteValue minus StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 19 , EndAbsoluteValue plus 7 , right parenthesis , right parenthesis minus 3 quarters StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 19 , EndAbsoluteValue plus 5 quarters StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 20 , EndAbsoluteValue minus 1 half StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , EndAbsoluteValue minus StartFraction, StartAbsoluteValue, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , EndAbsoluteValue Over 4 left parenthesis, StartAbsoluteValue, "t" , EndAbsoluteValue minus 21 , right parenthesis , EndFraction plus .5sine left parenthesis, StartFraction, pi Over 4 , EndFraction left parenthesis, StartAbsoluteValue, "t" minus 21 , EndAbsoluteValue minus StartAbsoluteValue, "t" minus 22 , EndAbsoluteValue plus 5 , right parenthesis , right parenthesis plus 1.5 1 3Yt=1−cosπk21−t−25t−25sinπ4t−t−2+t−2−t−4−1t−44t−4+51612t−4−t−6+1.24−2t−6+2t−7−2sinπ4t−7−t−8−17+12t−8−t−9−12+sinπ2t−9−t−10+4+4.924t−102t−10−72t−10+72t−11+7t−112t−11−6.0072t−11+6.0072t−12+29t−1216t−12−2.5cosπ2t−12−t−13+1−1t−132t−13+32t−13−32t−14−t−14+t−15−t−15t−15+.5cosπt−17−t−18−1t−182t−18+12sinπ4t−18−t−19+7−34t−19+54t−20−12t−21−t−214t−21+.5sinπ4t−21−t−22+5+1.513