$ x(t) = \displaystyle\sum_{k=-\infty}^{\infty}( a_k \cos 2 \pi \nu_k t + b_k \sin 2 \pi \nu_k t )$

x_t = @SUM( a_k * cos(2 * pi * nu_k * t ) + b_k * sin(2 * pi * nu_k * t , -infty, infty)

$ \nu_k = \displaystyle\frac{ k }{ T }$

nu_k = k / T

$ a_k = \displaystyle\frac{1}{ T } \displaystyle\int_0^T x(t) \cos(2 \pi \nu_k t ) dt$

a_k = @INT( x( t ) *cos(2* pi * nu_k * t )/ T , t , 0 , T )

$ b_k = \displaystyle\frac{1}{ T } \displaystyle\int_0^T x(t) \sin(2 \pi \nu_k t ) dt $

b_k = @INT( x(t) *sin(2* pi * nu_k * t )/ T , 0 , T )

$ a_k = \displaystyle\frac{1}{ T } \displaystyle\sum_{n=0}^{ N -1} x_n \cos(2 \pi \nu_k n \Delta t )$

a_k = @SUM( x_n *cos(2* pi * nu_k * n * Dt )/ T , n , 0 , N -1 )

$ b_k = \displaystyle\frac{1}{ T } \displaystyle\sum_{n=0}^{ N -1} x_n \sin(2 \pi \nu_k n \Delta t )$

b_k = @SUM( x_n *sin(2* pi * nu_k * n * Dt )/ T , n , 0 , N-1 )

$ x_n = \displaystyle\sum_{k=0}^{N-1} X_k e^{ i 2 \pi \nu_k n \Delta t }$

x_n = @SUM( X_k * exp(2 * pi * nu_k * t ), k , 0, N -1)

$ X_k = a_k - i b_k $

X_k = a_k - i b_k

$ X_k = \displaystyle\frac{1}{ T } \displaystyle\int_{0}^{ T } x(t) e^{ i 2 \pi \nu_k t } dt$

X_k = @INT( x( t ) *cos(2* pi * nu_k * t )/ T , t , 0 , T )

$ X_k = \displaystyle\frac{1}{ T } \displaystyle\sum_{ n =0}^{ N -1} x_n e^{ i 2 \pi \nu_k n \Delta t }$

X_k = @SUM( x_n *exp( i *2* pi * nu_k * n * Dt / T ), n , 0 , N -1 )/ T

$ r_k = \sqrt{ a_k ^2 + b_k ^2}$

r_k = sqrt( a_k ^2 + b_k ^2)

$ \phi_k = \arctan\displaystyle\frac{ b_k }{ a_k }$

phi_k = atan( b_k / a_k )