"Assume six progressively wider unity height pulses approximating one 90 degr~
ee"

"quadrant of a sinewave."

"Starting and ending angles of each pulse in degrees are..."

pa:=[7.07165,7.93585,21.2368,23.7716,35.4843,39.5217,49.8712,55.14,64.436,70.~
5768,79.1992,85.799]

"Assume an "*integrating*" filter with response of 1/H or 1/f ."

"1. What is the absolute fundamental  amplitude?"

"2. What is the relative strength of odd harmonics 3 through 19 compared to t~
he"

"fundamental?"

"3. What is the total harmonic distortion 3-19 in percent?"

f1(t):=-SUM((-1)^i*STEP(t-pa SUB i),i,1,DIM(pa))

f2(t):=f1(t)+f1(180-t)-f1(t-180)-f1(360-t)

f2(t)

FOURIER(y,t,t1,t2,n)

FOURIER(f2(t),t,0,360,19)

;Approx(User)
-0.0001383746245236238318453882747948468684831903263301862490606891819*SIN(0.~
0523598775598298873077107230546583814032861566562517636829157432*t)+0.4428871~
511277603067650870586765989531723385462904804607139974098*SIN(0.0174532925199~
432957692369076848861271344287188854172545609719144*t)-0.00010391043491255688~
12336107348300572466137932047430129392821135654*SIN(0.29670597283903602807702~
74306430641612852882210520933275365225448*t)-0.000115085341074297387556671972~
7941703127605094130237604327294080905*SIN(0.226892802759262845000079799903519~
6527475733455104243092926348872*t)+0.0002058765192983102516583106689754347924~
922706274511223803567646756*SIN(0.2617993877991494365385536152732919070164307~
83281258818414578716*t)+0.000191866966090628719657863059732246416782089264594~
1159675055750389*SIN(0.331612557878922619615501246012836415554145658822927836~
6584663736*t)

FOURIER(y,t,t1,t2,n):=1/(t2-t1)*INT(y,t,t1,t2)+2/(t2-t1)*SUM(COS(2*pi*m_*t/(t~
2-t1))*INT(y*COS(2*pi*m_*t/(t2-t1)),t,t1,t2)+SIN(2*pi*m_*t/(t2-t1))*INT(y*SIN~
(2*pi*m_*t/(t2-t1)),t,t1,t2),m_,1,n)

FOURIERV(y,t,t1,t2,n):=APPEND([1/(t2-t1)*INT(y,t,t1,t2)],2/(t2-t1)*VECTOR([IN~
T(y*COS(2*pi*m_*t/(t2-t1)),t,t1,t2),INT(y*SIN(2*pi*m_*t/(t2-t1)),t,t1,t2)],m_~
,1,n))

H:=FOURIERV(f2(t),t,0,360,19)

APPROX(VECTOR(H SUB i SUB 2/(i-1)/H SUB 2 SUB 2,i,4,DIM(H),2),6)

;Approx(User')
H:=[0,[0,0.4428871511277603067650870586765989531723385462904804607139974098],~
[0,0],[0,-0.00013837462452362383184538827479484686848319032633018624906068918~
19],[0,0],[0,9.34073258268070457918162684590399338773109035097054076518334526~
3*10^(-5)],[0,0],[0,-5.391856045322089176454503547076725940800328445218382922~
056970619*10^(-5)],[0,0],[0,-3.2347888352831868279742017360182068034479256134~
81990547589437023*10^(-5)],[0,0],[0,7.458667381919476246378799990541455356726~
314820410740775999461497*10^(-5)],[0,0],[0,-0.0001150853410742973875566719727~
941703127605094130237604327294080905],[0,0],[0,0.0002058765192983102516583106~
689754347924922706274511223803567646756],[0,0],[0,-0.000103910434912556881233~
6107348300572466137932047430129392821135654],[0,0],[0,0.000191866966090628719~
6578630597322464167820892645941159675055750389]]

;Simp(#19)
[-0.000104145,4.2181*10^(-5),-1.73919*10^(-5),-8.1154*10^(-6),1.531*10^(-5),-~
1.99886*10^(-5),3.099*10^(-5),-1.38012*10^(-5),2.28009*10^(-5)]

ABS([-0.000104145,4.2181*10^(-5),-1.73919*10^(-5),-8.1154*10^(-6),1.531*10^(-~
5),-1.99886*10^(-5),3.099*10^(-5),-1.38012*10^(-5),2.28009*10^(-5)])

;Approx(#22)
0.0001236868229884655093771264362011741615605434631872911146435636441