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in mixed (digital and analogue application) where you have to convert a signal from continuous to digital time domain and then back again to continuous time an anti-aliasing LPF is needed and in general also a LP reconstruction filter.

Are there some applications (if so what are) in which the reconstruction filter is not needed or not strictly necessary?

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  • $\begingroup$ If your output sample rate is high enough, you might not need a filter. $\endgroup$ – Jason R Aug 18 '14 at 17:12
  • $\begingroup$ For example consider a sampling frequency fs. The output samples are generated at the same rate so that in a time interval I have the same number of samples for the sampled input signal and for the generated output sample signal. In this case? Where can I find a reference about this fact? $\endgroup$ – Francesco Boi Aug 18 '14 at 17:18
  • $\begingroup$ So is your question about a direct connection of DAC and ADC (without filters)? Or is it about omitting the reconstruction LP after DAC but keeping the anti-aliasing LP before ADC? $\endgroup$ – Deve Aug 19 '14 at 7:22
  • $\begingroup$ It is about keeping the anti-aliasing LP before the analogue to digital conversion but omitting the LP after digital to analogue conversion $\endgroup$ – Francesco Boi Aug 19 '14 at 7:44
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If the system naturally has only a low enough frequency response (say a very heavy object relative to the forces involved), and the noise tolerance is high enough, then the effects of any aliasing, due to the lack of any additional low-pass and anti-aliasing filtering, may already be rolled-off below your desired or required noise floor.

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While the lowpass (LP) before analog-to-digital conversion (ADC) is generally required in order to avoid aliasing effects the reconstruction lowpass after digital-to-analog conversion (DAC) can be omitted if the bandwidth of the analog signal is allowed to have a high bandwidth.

In radio communication systems the reconstruction LP is very important because neighbouring channels must not be distorted and bandwidth is a valuable ressource. Thus the transmit signal (1) bandwidth should be as low as possible.

But especially if you transmit your signal over a lowpass channel (e.g. wireline) and you have no frequency-multiplexed signals the reconstruction LP might be avoidable. I would consider the following points for the decision

  • What's the bandwidth of the DAC output signal?
  • Is there an amplifier after the DAC? Can it handle high frequencies?
  • Is a modulator used? Can it handle high frequencies?
  • Are there any other signals on the transmission medium and can they get distorted by your transmit signal?
  • Are there non-linear components that could cause mixing of higher frequencies into the baseband (i.e. into the usefule frequency band)?

As it has been noted before, some components of your transmitter (DAC, Amp, ...) or the channel might already reduce the bandwidth of your signal considerably so that an additional LP is not required.


(1) With transmit signal I mean the analogue signal.

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No it not always needed.
For example in sound application that some weird sound is acceptable (not intended at DSP level).
Lets say I make up some sound using 8-bit microcontroller (without dedicated DSP module or DAC). I can just use R-2R Ladder to generate analog output from normal digital output pin. The output will not smooth at all but it is acceptable (It's art).
Depend on application requirement sometimes you may not need it.

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  • $\begingroup$ For example consider a sampling frequency fs. The output samples are generated at the same rate so that in a time interval I have the same number of samples for the sampled input signal and for the generated output sample signal. I am using the generated signal (which is a white noise process) to excite an actuator and the signal at the sensor is recorded. I am using these signals to identify the underlying model. In this case can I avoid it? $\endgroup$ – Francesco Boi Aug 18 '14 at 17:41
  • $\begingroup$ Avoid what? I understand you up to the word "sample signal". After that I read it as you generate white noise and feed it to the sensor. The sensor then active the actuator. And I cant extract any info beyond this point. If you want to inspect some linear black box how about feed something that resemble impulse signal to the system and capture the output signal? $\endgroup$ – Curious Sam Aug 18 '14 at 18:05
  • $\begingroup$ I meant avoid the usage of the reconstruction filter, independently on the excitation signal I use. $\endgroup$ – Francesco Boi Aug 18 '14 at 18:08
  • $\begingroup$ @Rorschach It is subjective for anybody beside ones who are in the project to decide if it need reconstruction filter or not but if you are generating the white noise I think you cant model a good reconstruction filter (for white noise) anyway. Note that I not fully understand you as I mentioned. $\endgroup$ – Curious Sam Aug 18 '14 at 18:16

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