# Thread: What do band pass filters do??? (Version 2)

Started: 2006-11-19 16:39:19
Last activity: 2006-11-19 16:39:19
Topics:
John or Jan Lahr
2006-11-19 16:39:19
I'm sending this again to correct the spelling of "sine" as in "sine
wave." "Sign waves" are what people do on the curb to generate
business for a car wash! http://www.mccullagh.org/db9/10/kids-car-wash.jpg
A sine wave is a mathematical function.
http://www.devx.com/assets/intel/9052.jpg

band pass filters and what they do? "

I'll take a stab at an answer and hope others will chime in as well.

Any seismic signal can be decomposed into an infinite set of sine
waves, each with a specific
amplitude and frequency. If all of the sine waves are added up, the
original seismogram will be
produced. Often the signal of interest has a low frequency and is
recorded with a low amplitude.
When viewed on the original seismogram, this small signal is buried
in higher-frequency, higher-
amplitude noise. In this case, if just the high frequencies are
reduced in amplitude by a "low-pass
filter," then the gain can be increased to boost the low frequencies
enough to become visible.

AmaSeis has two filters, a high-pass filter and a low-pass filter.

A "high-pass filter" allows frequencies higher than a set corner
frequency to pass unchanged, while attenuating lower frequencies.

A "low-pass filter" allows frequencies that are lower than a set
corner frequency to pass unchanged, while attenuating higher frequencies.

When both filters are set, the filter is called a "band pass" filter.

The corner frequencies can be adjusted by specifying either the
frequency or the period of the corner. The period is just 1 divided
by the frequency. For low frequencies, such as 0.05 Hz, it's easier
to think in terms of period -- in this case 1/0.05 = 20 seconds period.

Since the AS-1 samples the amplitude of the seismic signal about 6
times per second, clearly high frequencies will not be well
represented. The highest frequency that it's theoretically possible
to record faithfully is one half of the sample rate. (For more
details on this, look up Nyquist Frequency,
http://en.wikipedia.org/wiki/Nyquist_frequency )

Therefore, the low pass corner setting for AmaSeis should never be
set to a frequency higher than 3 Hz.

In order to enhance the surface waves, which have a lot of energy in
the range of .05 Hz (20 seconds period), I find it useful to set the
helicorder filters to pass the band from 12s to 25s. In other words,
the low-pass filter corner is set to 12 seconds and the high-pass
filter corner is set to 25 seconds.

Try these settings on today's record to see the effect on your
station. Keep in mind that the filter settings do not change the
data that are stored on disk, but simply change the way they are displayed.

To see what a broad-band research station looks like unfiltered,
low-pass filtered, and high-pass filtered, click on this image to
toggle between the three views:
http://www.jclahr.com/science/psn/cor/index.html

There is a interactive applet that demonstrates filtering of a signal
that consists primarily of just two frequencies. The band-pass
filter bands can be adjusted to "bring out" each of the frequencies
by itself. In the case of seismology, the lower frequency would be
so small that it would be hard to see prior to filtering out the
higher frequency and raising the
gain. See: http://www.chem.uoa.gr/applets/AppletFourAnal/Appl_FourAnal2.html

Hope this helps. Keep the questions coming!

John

12:07:50 v.c03ec7af