CLS
DIM Q(10)
DIM R(10)
REM ==FOURIER SERIES ANALYSIS OF PERIODIC FUNCTIONS==
REM ==INPUT DATA==
GOSUB [THTHZE]
REM ==INITIALIZE VARIABLES==
GOSUB [ONZENIZE]
REM ==COMPUTE L + 1 COEFFICIENTS==
L1 = L + 1
FOR J = 1 TO L1
J1 = J -1
W = W0 * J1
G = F0 * J1
REM ==M IS NUMBER OF INTERVALS FOR NUMERICAL INTEGRATION==
M = N8 * J
M1 = M -1
H = (X1 -X0) / M
H2 = 2 * H
REM ==COSINE COEFFICIENT A==
IF K8 = 2 THEN [ONNIZE]
IF K9=1 THEN
 GOSUB [ONSESIZE]
END IF
IF K9=2 THEN
 GOSUB [ONTHSIZE]
END IF
A = U * S / T
IF ABS(A) > 1/10^8 THEN [ONEIZE]
A = 0
REM ==SINE COEFFICIENT B==
[ONEIZE]
IF K8 = 1 THEN [TWTHZE]
[ONNIZE]
IF K9=1 THEN
 GOSUB [ONNIFIZE]
END IF
IF K9=2 THEN
 GOSUB [ONFISIZE]
END IF
B = U * S / T
IF ABS(B) > 1/10^8 THEN [TWTHZE]
B = 0
REM ==PRINT RESULTS==
[TWTHZE]
PRINT
PRINT "FOR N   =";J1
PRINT "W       = ";W
PRINT "W/TWOPI = ";G
PRINT "A       = ";A
PRINT "B       = ";B
PRINT
NEXT J
GOTO [TWONFOZE]
REM ==INPUT ROUTINE==
[THTHZE]
PRINT
PRINT "FOURIER SERIES ANALYSIS OF"
PRINT
PRINT "PERIODIC FUNCTIONS": PRINT:PRINT
PRINT "DEFINITION OF FUNCTION F:"
PRINT
PRINT "TYPE 1 : DEFINED IN FUNCTION F(X)"
PRINT
PRINT "TYPE 2 : PIECEWISE LINEAR"
PRINT
INPUT "TYPE= ";K9
PRINT
PRINT "INTERVAL OF EXPANSION"
PRINT
PRINT "X0 < X < X1"
PRINT
INPUT "X0 =";X0
PRINT
INPUT "X1=";X1
PRINT
PRINT
PRINT "TYPE OF EXPANSION"
PRINT
PRINT "TYPE 0 : GENERAL"
PRINT "TYPE 1 : COSINE ONLY"
PRINT "TYPE 2 : SINE ONLY"
INPUT "TYPE=";K8
PRINT
PRINT "DESIRED NUMBER OF TERMS"
PRINT
INPUT "IN EXPANSION = ";L
IF K9 = 1 THEN [ONZEEIZE]
PRINT
PRINT
PRINT "F(X) DEFINED AS PIECEWISE LINEAR"
PRINT
INPUT "NUMBER OF SEGMENTS = ";N1
PRINT
PRINT "ENTER END POINT COORDINATES X,Y"
PRINT "(IN ORDER OF INCREASING X)"
PRINT
N2 = N1 + 1
FOR I = 1 TO N2
PRINT "POINT";I
PRINT
INPUT "X = ";QQ
Q(I)=QQ
INPUT "Y = ";RR
R(I)=RR
PRINT
NEXT I
[ONZEEIZE]
RETURN
REM ==INITIALIZATION==
[ONZENIZE]
P1 = 3.1415926538
P2 = 2 * P1
U = 2
T = X1-X0
A = 0
B = 0
N8 = 20
IF K8 = 0 THEN [ONTWZEZE]
REM ==DOUBLE PERIOD FOR HALF EXPANSIONS==
T = 2 * T
U = 2 * U
PRINT
[ONTWZEZE]
PRINT
PRINT "PERIOD = ";T
PRINT
PRINT
PRINT "FOURIER COEFFICIENTS"
PRINT "********************"
PRINT
PRINT
FO = 1 / T
W0 = P2 * F0
IF K9 = 1 THEN [ONTHTHZE]
GOTO [ONTHFIZE]
[ONTHTHZE]
Y0 = F(X0)
Y1 = F(X1)
[ONTHFIZE]
RETURN
REM ==COSINE COEF. FOR F(X) PIECEWISE LINEAR==
[ONTHSIZE]
A1 = 0
J3 = 0
[ONTHEIZE]
J3 = J3 + 1
IF J3>N1 THEN [ONFIFOZE]
J4 = J3 + 1
X0 = Q(J3)
X1 = Q(J4)
E = X1 -X0
IF E = 0 THEN [ONTHEIZE]
Y0 = R(J3)
Y1 = R(J4)
D = Y1-Y0
P = D / E
H = E / M
H2 = 2 * H
REM ==PERFORM INTEGRATION==
GOSUB [ONSESIZE]
A1 = A1 + S
GOTO [ONTHEIZE]
[ONFIFOZE]
S = A1
RETURN
REM== SINE COEF. FOR F(X) PIECEWISE LINEAR==
[ONFISIZE]
B1 = 0
J3 = 0
[ONFIEIZE]
J3 = J3 + 1
IF J3 > N1 THEN [ONSEFOZE]
J4 = J3 + 1
X0 = Q(J3)
X1 = Q(J4)
E = X1 -X0
IF E = 0 THEN [ONFIEIZE]
Y0 = R(J3)
Y1 = R(J4)
D = Y1 -Y0
P = D / E
H = E / M
H2 = 2 * H
REM ==PERFORM INTEGRATION==
GOSUB [ONNIFIZE]
B1 = B1 + S
GOTO [ONFIEIZE]
[ONSEFOZE]
S = B1
RETURN
REM ==NUMERICAL INTEGRATION (SIMPSON'S RULE) FOR COSINE
[ONSESIZE]
S1 = 0
S2 = 0
T1 = X0
T2 = T1 + H
FOR I = 1 TO M1 STEP 2
D1 = COS(W * T1)
D2 = COS(W * T2)
F1 = F(T1)
F2 = F(T2)
S1= S1+ D1* F1
S2 = S2 + D2 * F2
T1 = T1 + H2
T2 = T2 + H2
NEXT I
Z0 =Y0 *COS(W* X0)
Z1 = Y1 * COS(W * X1)
S = 2 * S1+ 4 * S2 -Z0 + Z1
S = S * H / 3
RETURN
REM ==NUMERICAL INTEGRATION (SIMPSON'S RULE) FOR SINE
[ONNIFIZE]
S1 = 0
S2 = 0
T1 = X0
T2 = T1 + H
FOR I = 1 TO M1 STEP 2
D1 = SIN(W * T1)
D2 = SIN(W * T2)
F1 = F(T1)
F2 = F(T2)
S1 = S1 + D1 * F1
S2 = S2 + D2 * F2
T1 = T1 + H2
T2 = T2 + H2
NEXT I
Z0 = Y0 * SIN(W * X0)
Z1 = Y1 * SIN(W * X1)
S = 2 * S1 + 4 * S2 -Z0 + Z1
S =S * H /3
RETURN
[TWONFOZE]
END
REM DEFINE FUNCTION F(X) HERE
REM==F(X)PIECEWISE LINEAR==
REM ***************************
FUNCTION F(X)
F = 2*SIN(X)+COS(X)
REM ***************************
END FUNCTION