If
is the nth-order Fourier approximation to f, and
is the nth-order Fourier approximation to g, and
are scalars, then the nth-order Fourier approximation to
is

.

Question

If 
  is the nth-order Fourier approximation to f, and 
  is the nth-order Fourier approximation to g, and 
  are scalars, then the nth-order Fourier approximation to 
  is 
  
.

Quizplus · Accepted Answer

The addition of scalars does not affect the Fourier approximation, so the nth-order Fourier approximation to the sum of two functions multiplied by scalars is simply the sum of the nth-order Fourier approximations of the functions multiplied by the respective scalars. Therefore, the nth-order Fourier approximation to 11edaba5_20ba_09ad_a975_f1743fac6719_TBMC1039_00 is equal to the sum of the nth-order Fourier approximations to f and g, multiplied by the respective scalars, which results in 11edaba5_20ba_09ae_a975_55f395e912af_TBMC1039_00.

If Is the Nth-Order Fourier Approximation to F, and F