A product in the Fourier domain is a convolution in the physical domain |

Look what happens to the coefficients when we multiply polynomials.

(1) | ||

(2) |

(3) | ||

(4) |

(5) |

The second way to visualize polynomial multiplication is simpler.
Above we did not think of *Z* as a numerical value.
Instead we thought of it as ``a unit delay operator''.
Now we think of the product *X*(*Z*) *B*(*Z*) = *Y*(*Z*) numerically.
For all possible numerical values of *Z*,
each value *Y* is determined
from the product of the two numbers *X* and *B*.
Instead of considering all possible numerical values
we limit ourselves to all values of unit magnitude
for all real values of .This is Fourier analysis, a topic we consider next.

12/26/2000