Question on ADC/Sampling and Images

Say I have a sensor that generates a signal of freq 30Hz and now when I sample this at 100Hz, which is above the 2fa;
The Nyquist criteria is satisfied. But the output of the sampler has lot of frequencies right i.e., 30Hz, 100-30=70, 100+30=130, 200-30=170, 230....

Now if I dont do any digital domain low pass filtering on the output of ADC to bandlimit it to 50Hz or (some bandwidth less than 70Hz, the first image); and instead directly pass it to a DAC , will my output be faulty? i.e., the output of DAC not same as input to ADC?

i.e., Is it mandatory to do a digital domain filtering on the output of ADC always to be able to reproduce the original analog input; even if the input to ADC has just one freq component?

As long as you have an analogue reconstruction filter after the DAC that cuts off below 100Hz it will work fine.

The reconstruction filter is never an optional part however.

Regards, Dan.

You certainly need an analog reconstruction (lowpass) filter after the DAC, but not necessarily a digital filter.

Hi,

sampling signal is always considered to be lower than the half of sampling frequency. (Exception is dedicated undersampling)

With an anti aliasing filter before the ADC you ansure this.
But the same is true for the digital data or the reconstructed DAC converted data.

But the output of the sampler has lot of frequencies right i.e., 30Hz, 100-30=70, 100+30=130, 200-30=170, 230....

Click to expand...

Now look at your frequencies. They are all higher than half of the sampling frequency. So they are considered as not valid.
If you run a FFT on your digitial data, then they are not shown. FFT output is max. the half samppling frequency.

Therefore after a DAC you nedd the above suggested reconstruction filter. If you you done everything right: (anti aliasing filter, constant sampling frequency at ADC, constant sampling frequency for DAC, reconstruction filter) Then you should see the same shape as before the ADC.

Usually there is a processing of the digital data within a microcontroller or DSP or so, but this will obviously affect shape of signal.

Klaus