[A complimentary Cc of this posting was sent to

John O'Flaherty

<(E-Mail Removed)>], who wrote in article <(E-Mail Removed)>:

> I think you are conflating the power in light intensity

> (I=Power/Asurf) with signal power. Once the intensity is mapped into a

> signal, signal power has its usual meaning. You can create signals of,

> for examples, stock prices or annual rainfall, and can investigate the

> power spectra of the resulting signals, without a power interpretation

> for the original data. And once you have a voltage signal, it doesn't

> matter what it originally represented, its power is proportional to

> voltage squared, referred to a standard 1 ohm impedance.
I'm afraid you use terminology outside of their usual bounds. There

is no such thing as "signal power", "power of a voltage signal" etc.

> >> dB = 10 * log ( Signal_voltage ^ 2 / Noise_voltage ^ 2 )

> >> dB = 2 * 10 * log ( Signal_voltage / Noise_voltage )

> >These squares/twos are as much misplaced/wrong as "S" in "RMS power".

> The squares, when applied to statistical analysis of signals, are

> correct.
There is no "correct" thing in statistics. For example, let me

restate what you say in more "truthful" form:

The math of the L2-norm is much less tricky than math of other norms

(in spaces of functions), since it is a Hilbert norm (as opposed to

more general Banach norms). Therefore, when taught to beginners,

L2-norms are prefered as the first topic to expose.

Some people are exposed only to the 101-part of the topic, so may

think that it is all there is...

In reality, the norm to use is dictated by the "physical meaning" of

the function. E.g., in context of the signal of a photo-sensor, the

meaningful norm is the L1-norm, since each measurement already

represents energy.

> For example, in a textbook*, the definition of rms SNR for a

> decompressed image vs. an original image is given as the square root

> of the _square_ of the row-column double sum of the pixel errors,

> divided by the number of pixels.
As you can guess, the extremely low quality of US textbooks is a

recurring topic at some dinner tables...

Hope this helps,

Ilya