How to set the sampling frequency for this filter+

I need to make a passive LP anti-aliasing filter(recommended cut off freq.).

Filtered signal from an hotwire-anemometer will be measured by DAQ has 100Meg input impedance.

The thing is that my sampling freq. twelve khz and I'm not sure it is fine enough. At which freq. should the stop band start? How to decide the adequate sampling freq. for this

to be updated...

• What is the bandwidth of your signal? – Mike May 28 '19 at 13:04
• You need a much steeper filter to reject high slew rate spectral wind-speed signal at Nyquist rate = 12kHz/2 = - 60dB for a 10 bit ADC – Tony Stewart EE75 May 28 '19 at 13:09
• @Mike Bandwidth 3.2kHz – cm64 May 28 '19 at 13:17
• Do you really need to measure how fast the wind is blowing 3200 times per second? If it is a pulse output (pulses per rotation) then a digital input is probably better than sampling it as though it were an analog signal. – JRE May 28 '19 at 13:35
• Had a look. A "hot wire anemometer" ought to provide a voltage proportional to wind speed. The question remains: Do you really need 3200 measurements per second of the wind speed? – JRE May 28 '19 at 13:38

When designing an anti-alias filter for a lowpass signal, you need to know

1) The sampling frequency fs
2) The signal bandwidth fb
3) The quality of the signal you want to achieve

Your passband goes up to fb. It should be flat enough for your application, you may not want it -3dB down at fb, you might want less attenuation. A Chebychev filter has controllable passband ripple.

Your stopband depth must be enough for the quality of the signal. If you want a maximum of 1% alias products, then a -40dB stopband will be sufficient (you could use less at certain frequencies). For 0.1% aliasing, you need -60dB stopband.

For a post-DAC filter, the stopband starts at fs-fb, and goes up to infinity.

For a pre-ADC filter, your stopband edge depends on exactly how you are going to use the data. There are three choices.

If you are going to do analysis only in the specified passband, then your stopband starts at fs-fb. Signals between fs/2 and fs-fb will alias to below fs/2, however they will be above fb, and if you are analysing only to fb, will not cause a problem.

If you want no signals aliased at all, even if they are out of your specified bandwidth, then your stopband should start at fs/2. This might be useful if signal harmonics are present, and they form part of your processing dynamics, for instance detecting zero crossings. Harmonics, when aliased, become non-harmonic, and mess up peaks and zero crossings.

If you want to do as little digital processing as possible, then your stopband should start as close to fb as you can economically make it.

• Im stuck with passive RC filter possibility at the moment only. Do you recommend to cascade RC filters? – cm64 May 28 '19 at 13:34
• It depends, have you read my answer? What's signal quality do you want? How are you going to be processing it? Cascading RCs doesn't work if they're all the same value, you need (let's say) 50ohms 1uF, followed by 500ohms 100nF, followed by 5k 10nF, to avoid loading of the first stage by subsequent stages. However this will give you -9dB at 3.2kHz, so it's 'better' to design a higher order filter. If however you're just trying different filters to see what they do for your signals, go ahead. Once you've got a stopband depth spec, you might look at stopband zeroes for a better filter shape. – Neil_UK May 28 '19 at 14:16
• Yes I read your answer and it is great. The thing is Im limited with passive way at the moment I dont have the components and split supply ect for the filter and have to build something quick and dirty for tomorrow.. Something better than nothing, – cm64 May 28 '19 at 14:24
• The question to ask yourself is 'what's wrong with the results of a single stage RC?' If there's too much aliasing, then cascading a second stage of 10x the impedance after the first would be a quick and dirty way of answering the question 'will another cascaded RC stage help?' – Neil_UK May 28 '19 at 14:56
• I need to understand one thing you wrote as “application, you may not want it -3dB down at fb, you might want less attenuation.” So if my BW is 3.2kHz I shouldn’t set the cut off at 3.2kHz. But what should the cut off be set around then? Thanks – cm64 May 28 '19 at 17:08

I understand that hot-wire-anemometers, HWA are used to study wind turbulence with very fast slew rates , where Tsr=0.35/f-3dB.

If you have a 12 bit ADC, any signal above the Nyquist rate and above your ADC resolution is aliasing noise.$$\Av(½f_s) = 20 log 2^{-12}=-72dB \$$ Now define your specs.

• $$\f_s= 12kHz\$$
• LPF stop band $$\f_{sb}= 6kHz @ -72dB\$$
• passband $$\f_{-3dB}=3.4kHz \$$ linear phase or Bessel to -12dB
• A Chebychev is steeper but will cause more ringing from high Q in the LPF due to a Heaviside Step Function from a wind shear or turbulence.
• Since this is less than 1 octave, I an expecting 72/-6dB/oct. = 12th order filter using a quad Op Amp and 12 Caps.

There are many tools to design easily as long as you know how to scale values and keep the same RC product and understand what group delay does to a step function.

• How about for 16 bit ADC? – cm64 May 28 '19 at 14:14
• Will the RC filter be useless or at least better than nothing'? I dont have time to make active filter:( I will consider when Im given time – cm64 May 28 '19 at 14:16
• WHat is $20 log 2^{-16}$ .. It takes only minutes to design a filter – Tony Stewart EE75 May 28 '19 at 14:16
• @sunnyskuy But I dont have the right components and split supply ect. If I order now it will take two days to receive. I need this urgent maybe I should cascade RC filters.. (I appreciate your answer it is useful for next time if I have the components ) – cm64 May 28 '19 at 14:21
• wrong... do it right or dont do it at all – Tony Stewart EE75 May 28 '19 at 14:22

if you just need to begin to examine the wavelengths and the energy distributions, then try this

simulate this circuit – Schematic created using CircuitLab

If you get too much attenuation at 3.2KHz, then reduce the downstream capacitors by about 50%, and re-measure.