Why are my DAC and ADC responses drooping?: Page 2 of 5

May 14, 2012 // By Kendall Castor-Perry
Why are my DAC and ADC responses drooping?
The Filter Wizard aka Kendall Castor-Perry turns his focus on to the troublesome problem of unexpected droop when dealing your DAC and ADC responses.

sample points, i.e. has a width equal to the sample interval.  Such a rectangular time response corresponds to a frequency response that has a sinc() characteristic.  sinc(x) is shorthand for sin(x)/x, and there’s a Fourier looking-glass correspondence between rectangular in one domain and sinc() in another that crops up all over the place, not only in signal theory but in the whole of physics.

Calculating the value of the sinc function – the value of the argument x is pi times the ratio of signal frequency to sampling frequency – shows that the droop is already -3 dB at around 0.444 times Fs.  Figure 1 shows the frequency effect of sinc() droop for a 1 per second sample rate.  Notice that it has deep but narrow notches at frequencies that are multiples of the sample rate.

Figure 2 shows a 0.444 Hz sinewave and also the result of sampling it once per second.  The peak value that is reached by a sample can clearly be the peak value of the input voltage.  But as the sample clock ‘walks’ over the signal there are regions where the output voltage is low for an appreciable period of time.

Figure  1:  The sinc() response of zero-order hold at 1 sample per second

Figure 2:  A 0.444Hz sinewave sampled – and held – at 1 sample per second    

Our 0.444 Hz signal is still present, but its level has been reduced, since some of the energy has been moved into higher frequency 'images', as shown in Figure 3.  You can see that the input signal's single Fourier component peeps up 3 dB above the value of the 0.444 Hz component in the output signal.

Figure 3:  Frequency spectra of the waveforms in Figure 2   

The take-away is that the peak-to-peak value of a sampled sinewave is not a good measure of the energy contained at the fundamental frequency.  As you increase the

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