Other Lp Norms

Since our main norm is the square root of a sum of squares,

we are using what is called an

We could equally well have chosen a *normalized
norm*:

which is simply the ``RMS level'' of (``Root Mean Square'').

More generally, the (unnormalized) *
norm* of
is defined as

(The normalized case would include in front of the summation.) The most interesting norms are

- : The , ``absolute value,'' or ``city block'' norm.
- : The , ``Euclidean,'' ``root energy,'' or ``least squares'' norm.
- : The , ``Chebyshev,'' ``supremum,'' ``minimax,'' or ``uniform'' norm.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University