digital lowpass filters and analog RC lowpass

Hi,

I am using a 40Hz -3dB RC lowpass filter, and then a 40Hz 1 pole digital lowpass (100Hz sampling butterworth generated from here: "

What is the effective -3dB frequency for the combination of these two filters? I don't think it is the same as a 2pole filter but am not sure.

Also is it possible to replace an analog lowpass filter with a digital lowpass for filtering out high frequency? ie. If I have a 100Hz sampling rate with the digital filter and a 40Hz -3dB frequency, will this filter be able to filter out signals above the sampling rate?

cheers, Jamie Morken

You have two cascaded filters. You can just multiply the two gain curves together, if the gains are in Volts per Volt, or add them together if they are in dB. Then you should easily be able to see where the new -3dB point is.

You are cutting things too close with respect to the Nyquist criterion. The Nyquist criterion says that you can't unambiguously reconstruct a signal from its samples unless the signal bandwidth is constrained within the range of n*f to (n+1)f, where f is half the sampling rate, and n is an integer. Half the sampling rate is sometimes called the Nyquist frequency, or just Nyquist.

The simple version of the rule (when n=0) is that you can't feed any signals greater than Nyquist to an ADC. According to the simple version of the rule, you need an analog low-pass filter in front of the ADC which guarantees that signals greater than Nyquist do not pass.

There is a trick, though, which doesn't break any rules. If you use an n other than 0, you can sample higher frequencies without ambiguity. You still would probably need an anti-aliasing filter, but it will now be a bandpass filter.

For example, you are sampling at 100 Hz, so if you had a signal which was band-limited so that all of the signal content was between 50 and 100 Hz, you could sample the signal, then later reconstruct it correctly by feeding the samples to a DAC and using an appropriate output filter.(I guess ideally you would want to interpolate, or take an FFT, zero-pad, then invert the FFT before going to the DAC, which would run at twice the ADC sample rate.)

But any time you could have signals at more than one Nyquist band, you will have problems, because you cannot differentiate them. For example, in your case, you have no way to differentiate a signal at 40 Hz from one at

So, in short, I don't think you can eliminate the analog filter. In fact, depending on your signal, it would probably be advisable to sample much faster or put a steeper analog filter in front of the ADC. Once you digitize your signal without violating Nyquist, you can implement any kind of digital filter you want.

If you are using any op-amps, it might be easiest to just cascade them to get a steeper cutoff for your analog filter. You can push the cutoff closer and closer to 50 Hz as you add more elements to keep the overall

-3dB point where you want it. If you keep the sampling rate at 100 Hz, you will want to have lots of attenuation at 50 Hz. The exact value will depend on the characteristics of your signal. Just keep in mind that anything above 50 Hz will alias back in at another frequency.

--Mac

The cutoff frequency will be around 28Hz, but the digital filter is useless, if you have any signal content above 50Hz with the analog filter only. If you want i.e. a 12bit accuracy up to 40Hz, make sure your input signal is attenuated by 72dB above 60Hz. It will be difficult to make an analog filter that steep, but alternativly you can increase your sampling frequency to say

So the analog filter can *not* be replaced if it is needed for aliasing purposes. But oversampling is the way to go.