Relatives to the Fourier Transform4-15which was found using the trigonometric relation: tan (A B) tan A tan B 1 tan A tan BIf we set u(x, y) constant, multiply (4.46) by p=T0 and then taking the tangent of both sides of the equation we obtain x 2 y 2 b2 2b y 0 constantp tan T0 or x 2 y 2 b2 Cby 0If, for example, we set b 1 and then change the values of the constant C, we produce a set of curves which indicate a constant potential or a constant temperature for heat problems. The following MATLAB1 program will produce the desired curve. Let b 1 and C 4, then we write in the command window: )pl 'x^2y^2-1-4*y'; )ezplot(pl,[4 4 0 8]); To produce additional iso-potentials you just change the value of C.&4.4 Finite Sine Fourier Transform and Finite Cosine Fourier TransformIf we assume 0 < t < l, then the ite sine Fourier transform (FFST) and its inverse ite Fourier sine transform IFFST transforms are deed as follows:l s (p) f (t) sin ppt dt F{ f (t)} F l D 0 1 2 X ppt F1 {Fs (p)} f (t) Fs (p) sin l p1 l(4:47)The ite cosine Fourier transform (FFCT) and its inverse (IFFCT) arel ppt D dt F{ f (t)} Fc (p) f (t) cos l 0 1 1 2 X ppt F1 {Fc (p)} f (t) Fc (0) Fc (p) cos l l p1 lor (4:48)
