IIR Filtering and response .vi: Butterwort​h filter magnitude response depends on sampling rate -why?

Question

Hi folks,
I am not expert in filter design, only someone applying them, so please can someone help me with an explanation?
I need to filter very low-frequent signals using a buttherwoth filter 2. or 3. order as bandpass 0.1 to 10 Hz .
Very relevant amplitudes are BELOW 1 Hz, often below 0.5 Hz but there will be as well relevant amplitudes above 5 Hz to be observed.
This is fixed and prescribed for the application.
However, the sampling rate of the measurement system is not prescribed. It may be between say between 30 and 2000 Hz. This will depend on whether the same data set is used for analysing higher frequencies up to 1000 Hz of the same measurement or this is not done by the user and he chooses a lower sampling rate to reduce the file sizes, especially when measuring for longer periods of several weeks.
To compare the 2nd and 3rd order's magnitude response of the filter I used the example IIR Filtering and response .vi:
I was very astonished when I the found that the magnitude response is significantly influenced by the SAMPLING RATE I tell the signal generator in this example vi.
Can you please tell me why - and especially why the 3rd order filter will be worse for the low frequency parts below 1 Hz of the signal. I was told by people experienced with filters that the 3rd oder will distort less the amplitudes which is not at all true for my relevant frequencies below 1 Hz.  
In the attached png you see 4 screenshots for 2 or 3 order and sampling rate 300 or 1000 Hz to show you the varying magnitude responses without opening labview.
THANK YOU for your ANSWERS!!!
chris
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Attachments:
butterworth-filter-differences.png ‏285 KB

Answer 1

Hello Lynn,
thanks for the answer. You are right that there are few points "behind" the curve in the graph, see png.
However, this is the filter response which Labview (2009) provides to me directly out of the "IIR Filter for 1 Channel. vi" in the "filter information" output cluster. Where up to now I do not know how to influence it - apart from adjusting the input parameters "IIR filter specifications". OK, I assume I have to gain more knowledge of this. The curve of the magnitude resonse dies not change when I change the number of samples of the input signal of the signal generator, only wehn I change the sampling rate.
I used directly the example vi from Labview with the name indicated in my first post "IIR Filtering and Response.vi".
So I assumed that everybody has it in his/her examples shipped with LV and it is not necessary to post it.
I just adjusted the size of the diagram of magnitude response to see the curves better as you see in the attached vi.
So I did no changes to the vital parts of signal generation and filter of the example. The screenshots are like they come from the example when using the option "one waveform" where I as user assume that this which is behind is quality-controlled by NI.
I was also astonished that the filter magnitude response is different to the one I copied out of graphs 1 year ago - but I unfortunately cannot reconstruct which example I used there...
Thanks for any further comments
chris
Attachments:
IIR Filtering and Response_CH.vi ‏55 KB
butterworth2nd_order_bandpass_0p1to10Hz_mag_response.PNG ‏18 KB