Antialising for digitizing systems
It's commonly known that a digital signal processing system requires an anti-alising filter before the A/D-conversion, and a number of sources in the literature are available on the subject. However, a few hints and good practices are worth mentioning to optimize the system and to unleash the full potential of the signal processing.
The required attenuation of an anti-aliasing filter should be specified from a frequency equal to the sampling frequency minus the maximum frequency of the signal-of-interest. This prevents signal components around the sampling frequency to get folded down into the digitized spectrum. The transition band of the anti-aliasing filter will get smaller and smaller the closer you want the maximum frequency of the signal-of-interest to the Nyquist frequency, and eventually, the order and thus the complexity of the required filter will skyrocket. As an example, if you want 20 kHz through a system with 44.1 kHz sampling, the transition band would go from 20 kHz to 24.1 kHz. A resolution of 16 bits would require an attenuation in the order of 100 dB, thereby needing something like a 13th or 14th order elliptic filter, hardly something you'd care to implement, manufacture or adjust. For this reason, a ratio between the sampling frequency and the maximum signal frequency this close to 2, compromises involving relaxed specifications would be required. Obviously, to ensure signal integrity without a too complex filter, the ratio between the sampling frequency and the maximum frequency of the signal-of-interest should be 3-4 or larger.
The required attenuation in the stop band of the anti-aliasing filter depends also on the level of the signals in the stop band. In case you have signals that are larger than full scale of the converter, you need to increase the attenuation similarly. Textbook examples seem to assume that the in-band and the out-band signals have the same magnitude, but that's an assumption you cannot afford to make.
Note that universal data acquisition gear does not typically include anti-aliasing filters, due to the diverging requirements of the different applications in which the gear may be used. In this case, you are responsible to add the right anti-aliasing filter.
It's commonly known that a digital signal processing system requires an anti-alising filter before the A/D-conversion, and a number of sources in the literature are available on the subject. However, a few hints and good practices are worth mentioning to optimize the system and to unleash the full potential of the signal processing.
The required attenuation of an anti-aliasing filter should be specified from a frequency equal to the sampling frequency minus the maximum frequency of the signal-of-interest. This prevents signal components around the sampling frequency to get folded down into the digitized spectrum. The transition band of the anti-aliasing filter will get smaller and smaller the closer you want the maximum frequency of the signal-of-interest to the Nyquist frequency, and eventually, the order and thus the complexity of the required filter will skyrocket. As an example, if you want 20 kHz through a system with 44.1 kHz sampling, the transition band would go from 20 kHz to 24.1 kHz. A resolution of 16 bits would require an attenuation in the order of 100 dB, thereby needing something like a 13th or 14th order elliptic filter, hardly something you'd care to implement, manufacture or adjust. For this reason, a ratio between the sampling frequency and the maximum signal frequency this close to 2, compromises involving relaxed specifications would be required. Obviously, to ensure signal integrity without a too complex filter, the ratio between the sampling frequency and the maximum frequency of the signal-of-interest should be 3-4 or larger.
The required attenuation in the stop band of the anti-aliasing filter depends also on the level of the signals in the stop band. In case you have signals that are larger than full scale of the converter, you need to increase the attenuation similarly. Textbook examples seem to assume that the in-band and the out-band signals have the same magnitude, but that's an assumption you cannot afford to make.
Note that universal data acquisition gear does not typically include anti-aliasing filters, due to the diverging requirements of the different applications in which the gear may be used. In this case, you are responsible to add the right anti-aliasing filter.
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In this example, showing an exponential averaging of a Loran-C signal on two separate channels with different low-pass filters, the difference is clear to see. Both channels run at 400 kHz sampling, and are sampled simultaneously. On channel 1 the bandwidth is limited by the receiving loop antenna only. On channel 2 a 7th order elliptic filter with cut-off around 110 kHz is used. This particular filter gives more than 86 dB attenuation above 300 kHz.
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As the out-of-band signals increase during night, the poorly filtered channel suffers even more.
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