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![]() | Waves and Fourier sums | ![]() |
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A product in the Fourier domain is a convolution in the physical domain |
Look what happens to the coefficients when we multiply polynomials.
The second way to visualize polynomial multiplication is simpler.
Above we did not think of as a numerical value.
Instead we thought of it as ``a unit delay operator''.
Now we think of the product
numerically.
For all possible numerical values of
,
each value
is determined
from the product of the two numbers
and
.
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.
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![]() | Waves and Fourier sums | ![]() |
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