A DATS user asked…
We are using the third octave band filter at very low frequencies (~1Hz) and I noticed that the response of the filter could introduce very significant errors for short or transient signals. Looking a bit more in details at the function, the help says:
“For audio work ISO standards use a reference frequency of 1kHz not 1Hz”
Does that implies that for non-audio work, a reference frequency of 1Hz should be applied? If yes, is it possible to change this reference frequency in the dats function?
Dr Mercer replied…
Essentially there is no problem and no need to change the reference frequency provided you use Base 10 mode and not Base 2. Base 10 is the ANSI S1.11-2004 preferred scheme.
The primary use of the reference frequency is to derive the true centre frequency, the true band edge frequencies and, the band number. The relationship between the exact centre frequencies between two 1/3 octave bands is a ratio. Thus when calculating exact as opposed to the preferred third octave centre frequencies we have to fix one frequency as definitely being the centre frequency of a third octave, and this is known as the as the reference frequency so that we can compute all the other frequencies exactly. For noise and vibration work, 1kHz is the normal reference frequency.
With Base 10 both 1kHz and 1Hz are actual centre frequencies so all is well. With Base 2, then 1kHz is still of course a centre frequency but the exact centre frequency closest to 1 Hz is 0.9765625Hz. This in turn creates a difference as to the band edge frequencies: for base 2 we have from 0.77571Hz to 1.096154Hz, and for base 10 the edges are at 0.794328Hz an d 1.122462Hz. For the usual audio frequencies there is generally no significant difference, but in your situation there is considerable difference.
One other advantage of base 10 is that there are the same number of frequency steps in each decade. Also in Base 10 1Hz is band zero, 1kHz is band 30 {1kHz = 10^3 so band number is exponent * 10} , 0.1 Hz is band -10 , and so on. Conversely if we know the 1/3 octave band number then the exact centre frequency is given by 10^(BandNumber/10).
If you use the time-based 1/3 Octave analysis there could be some unintended consequences. That technique uses the exact filter method. As explained below if your transient is very short you can be just measuring the characteristics of the filter.
Very narrow filters such as 1/3 octave around 1Hz are not good for measuring the response to transients. At 1Hz you have a filter of bandwidth of about 0.23Hz. The rise time of a filter is defined as the time taken to rise from 10% to 90% of the amplitude of a step input. For a simple single pole filter, such as an RC filter, the rise time is approximately (0.35/bandwidth) so with a 0.23 Hz band width the rise time is something like 1.5 seconds. I have made up a very simple test worksheet for you so you can see the effects of bandwidth and number of poles in the filter (In DATS terms 1 pass is 2 poles). This worksheet creates a step signal with the step at 1 second. I have left it with a simple 1 pass set up using a Butterworth low pass filter (it is band width not whether it is low, high or band pass configuration). With this you will see the rise time is also about 1.5 seconds but the time to reach the 90% from the start of the pulse is about 1.8 seconds, and for the oscillations to die out is a steady output is around 5 seconds from pulse start. Now to meet ANSI requirements for Class 1 filtering it is necessary to use 6 pole (3 passes) Butterworth filters. So setting the number of passes on the lowpass butterworth to 3 gives a rise time of about 2.85 seconds, 3.7 seconds from and up to 15 seconds to full stable output.
Alternatively, if you use the FFT based third octave method to get a reasonable estimate for a 0.23 HZ bandwidth you need a frequency resolution around 0.07Hz, and this in turn would need a minimum sample time of around 15 seconds. Remember the FFT finds the average amplitude over the whole period. So if your transient lasts say for 1 second it is most likely that your measured amplitudes will be typically 1/15 or less of their true amplitude or at least 20dB too low!
Basically be very careful at measuring transients with third octave filters at low frequencies.
Click to download the worksheet for DATS V7
Dr Colin Mercer
Latest posts by Dr Colin Mercer (see all)
- Data Smoothing : RC Filtering And Exponential Averaging - January 30, 2024
- Measure Vibration – Should we use Acceleration, Velocity or Displacement? - July 4, 2023
- Is That Tone Significant? – The Prominence Ratio - September 18, 2013
