michael brown wrote:
>This may sound like a dumb question, but I have not run across a good
>"plain
>English" description of low-pass [...]

A time-varying signal can be represented as a function of time, f(t).
The same function can be represented in "frequency space" via a linear
transformation called the Fourier transform as F(w), which tells you
how much sinusoidal component the original function has at each
frequency w (read as omega). If you know much linear algebra, you can
think of f(t) and F(w) as being vectors related through a change of
basis, though of course we are talking here about an infinite-
dimensional function space rather than the (possibly) more familiar
finte-dimensional euclidean vector space. A low-pass filter is very easy
to define in frequency space: it lets through the low-frequency
components but blocks the high-frequency components. Mathematically,
you Fourier transform the original function, multiply by the filter
function (as represented in frequency space), then invert the Fourier
transform to get the filtered time-varying signal.

Hm, this isn't really "plain English" is it? Try again.

A low-pass filter lets the slowly-varying part of a signal through,
but blocks the quickly-varying part. Like, if you had a 1kHz wiggle
superimposed on 60Hz mains voltage, then after filtering with an
appropriate low-pass filter, you would recover the 60Hz part with the
1kHz wiggle blocked out. A simple low pass filter is a resistor
followed by a capacitor to ground:

  Vin o----^v^v^v---*-----o Vout
        (Resistor)  |
                   ---
                   --- (Capacitor)
                    |
  GND o-------------*-----o GND

(Please excuse my hideous ASCII "graphics"). The capacitor serves to
shunt any high-frequency component of Vin to ground (a capacitor has
low impedance to high-frequency, high impedance to low-frequency). It
is easy to show that the 3dB point of this filter is at 1/(2 pi R C).
In frequency space, this simple filter falls off at higher frequencies
rather gently: it is not a very precise low-pass filter. For better
filtering you can use active filters.

Was this in the least bit useful? I hope so.

Michael V

Thank you for reading my "little" posting.


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