Full transcript
0:00Hello everybody. Today we'll talk about
0:01how do we convert a 1/3 octave spectrum
0:04to a 1x one octave spectrum. So to
0:06introduce an octave band is a frequency
0:09band that spans one octave. Each octave
0:11band covers a specific range of
0:13frequencies. There are different types
0:14of octave bands just 1x one octave, 1/3
0:17octave, 112th and so on. So the 1x one
0:20octave band is like an entry- level
0:22octave band which provides lesser
0:24frequency resolution and the higher
0:26octave band such as 1/3 1612th and so on
0:29provide higher resolution but they also
0:31consume more data. So let's say you have
0:34like a higher resolution octave band you
0:36wish to convert to a lower resolution.
0:38How do you go about it? Let's see that
0:40in detail. So let's say you have a 1/3
0:42octave spectrum. You have captured the
0:44data processed it and you have this 1/3
0:47octave spectrum. So on the y- axis is
0:49the sound pressure level in dba and on
0:51the x-axis you have this octave
0:53frequencies. Now I've chosen from 25 htz
0:55to 20,000 htz. There are frequencies
0:58beyond and below this but they are out
1:00of the human hearing range. So I've just
1:01included this bands. So let's say this
1:03is the frequency band. Let's view it in
1:06a tabular form. So the same information
1:08we are viewing it in a table form. So we
1:11have the frequencies from 25 htz all the
1:13way up to 20,000. And these are the
1:15levels for each of those frequency
1:17bands. So as you can see here, octave
1:191/3 is a higher resolution frequency
1:21band. So you have a lot more
1:23frequencies. But when you look at octave
1:251x1, it has only 10 frequency bands
1:28because it offers lower frequency
1:30resolution.
1:32So you have uh from 31.5 to 16,000. But
1:35when you look here, you have like 25 to
1:3820,000. So it provides three times more
1:40resolution than the octave one by one.
1:42Now let's look at the frequency
1:43relations. We know that octave 1x1 has
1:4610 frequency bands from 31.5 to 16,000.
1:49But octave 1/3 is you know higher
1:52resolution octave bands. So as the name
1:54suggests 1/3 is like splitting each
1:56octave 1x1 band to three equal parts. So
1:59for example here we have 31.5 in octave
2:021x 1 but in octave 1/3 the same 31.5 is
2:05split into 25 31.5 and 40. So you get
2:09higher resolution. So you have more
2:11resolution. If you have just octave 1x1,
2:13you only see 31.5. But now here you can
2:16see even these frequencies. So this
2:18works for other higher resolutions as
2:20well. For example, octave 16. You're
2:22dividing each octave 1 by one to six
2:24equal parts. So with this idea, we can
2:27actually compute, you know, actually
2:29convert a higher frequency resolution
2:31octave band to a lower frequency
2:32resolution. How do we go about it? It's
2:34simple. It's you just take these values
2:37the sound pressure level for each of
2:38these frequencies and add them up
2:40logarithmically to get the sound
2:42pressure level for this value. So you
2:45add them up logarithmically. The
2:47logarithmic equation is as shown here.
2:49So we have three values here 25 31.540.
2:53Just plug in those sound pressure levels
2:55here here and here and you get the final
2:58answer which is a logarithmic addition
3:00of all these frequency bands. Now the
3:02same process can be repeated for each of
3:04those pairs of frequency bands. So after
3:06logarithmic addition we have the sound
3:07pressure level values for each of the
3:09octave 1x1 frequency bands from 31.5 to
3:1216,000 which we can plot on a graph and
3:14view the octave 1x1 spectrum which was
3:17calculated from the octave 1x3 spectrum.
3:19So you can repeat this process for
3:21higher resolution octave bands as well
3:23just 16 1124. The only difference is the
3:26calculation time is going to exceed a
3:28lot because in this case we just added
3:31three bands to get one band. But in case
3:33of octave 1x six you're going to add six
3:35bands to get one band and so on and so
3:37forth. All right, thank you for watching
3:39this video. I hope you enjoyed it. Have
3:40a great day.