## PSN-L Email List Message

Subject: Re: FFT
From: "Randall Pratt" randallpratts@..........
Date: Fri, 11 Aug 2000 14:22:09 -0500

```I have a good example of Nyquist frequency behavior in an FFT.
I used EMON and substitued the collect routine with a function
y=250*sin(m*data point number).  In other words, each point was on a pure
sine wave and in sync with the sample rate.  At the rate of 8.46 samples/sec
this resulted in a basic sine wave period of 42.5532 seconds.  I then slowed
the sample rate by averaging 6 samples per point giving a sample rate of
1.41sps but the wave period remained the same with m=1.  Next I incremented
m to 20, 40, 60, 80 to effectively increase the frequency by those
multiples.  I have posted the data file nyquist.fft at
http://www.santel.net/~randallpratts/ if you want to play with it.  Starting
with m=20 or 20* the basic frequency we would expect the period to be
2.1277sec and we measure 2.131 from FFT.  Here we would have 3 data points
per cycle.  The next frequencies are above Nyquist and have fewer than 2
data points in a complete sine wave.  The expected frequency goes up and the
FFT measured frequency goes down.  Notice how both 20 times and 60 times the
basic frequency look the same on the FFT.  Once the high frequency is
aliased in I don't know how it could be filtered out.  Someone else may

rn Measured period freq ratio theory ratio expected period meas/exp
points/cycle
20         2.145         1.0000         20.00         2.1277
1.01             3.00
40         1.429         1.5010         40.00         1.0638
1.34             1.50
60         2.145         0.6662         60.00         0.7092
3.02             1.00
80         4.293         0.4997         80.00         0.5319
8.07             0.75

Sample rate/2  0.705 sec Nyquist period
1/cutoff  1.42

Randy

----- Original Message -----
From: "Barry"
To:
Sent: Sunday, August 11, 2002 9:25 AM
Subject: Re: FFT

> Rolando
>     I'll contribute a little. As I understand it, any signal can be
> representated by a sum of sine waves of different frequencies and
> magnitudes. With the FFT, the math routine has selected multiples of 2 to
> speed up the calculation process. You  don't get as much of the frequency
> spectrum but it calculates faster. What you  see when you run an FFT is
the
> magnitude sum of the various sign waves ploted as a function of frequency
> for that given quake and your sensor.  I, as an example,  usually filter
> teleseismic events to remove frequencies below 0.003 hz and above 0.5 to 1
> hz ( so my files won't be so large.) . You should save events at a
sampling
> frequency twice the value of the highest frequency  of interest
(Nuquest ).
> I think what happens if you save higher frequencies than the sampling
rate,
> the sampling picks  points on different signal cycles (like a beat) and a
> higher frequency can look like a low one in the FFT.
> Regards
> Barry
>
> > > Larry et al,
> > > I am a newcomer -almost- in this list and an apprentice of the
> earthquakes
> > > sciences, I have been posting events at the PSN web page since late
May,
> > > having the good fortune to live in the middle of a very active area, I
> > have
> > > posted a few. As a beginner I need to learn a lot about many things, I
> > have
> > > received wonderful help from several PSN members, thank to them I am
> > > enjoying this very much. I would like to address some questions to the
> > group
> > > looking for some light in the area of what the FFT module of WINQUAKE
> is,
> > > I've used the filters in a very practical and blind way, so I have a
> > slight
> > > idea of what it can be used for,  but have no clue in the relationship
> > among
> > > the period of sensor and the freq of the event and the proximity of
> quake,
> > > etc, and the FFT screen, so I really need further assistance. Can
> someone
> > > give me some light, please? How can I find some info in the Internet,
> > book,
> > > etc.,? Your help would be very appreciated.
> > > Best regards from Fraijanes, Guatemala.
> > > Rolando Benitez
> > >
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