8 ms·

> You also sample at a rate > to the centre frequency To be clear, a sampling rate that is only greater than the center frequency isn't very useful. You need t

by zild3d 10y ago

> You also sample at a rate > to the centre frequency To be clear, a sampling rate that is only greater than the center frequency isn't very useful. You need the well known nyquist rate, twice the maximum frequency to avoid aliasing https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampli...

nickff 10y ago
Your actual sampling rate will be higher than the Nyquist if you are trying to process data from an array, as the sampling rate required to detect phase shifts depends on the sampling period (which is determined by how quickly you want to 'move' the array).
cnvogel 10y ago
This is not strictly true. You can reproduce a band-limited signal as long as the bandwidth of this signal is smaller than half the sampling frequency. For example, a signal that only has energy in the range of 9MHz to 11MHz has a center frequency of 10MHz, but a Bandwidth of 2 MHz. You could sample, and reconstruct, the signal perfectly with a sample-rate higher than 4 MHz. Any content between DC and 9MHz that would be present would distort the sampled waveform, though, and create artifacts. https://en.wikipedia.org/wiki/Undersampling https://en.wikipedia.org/wiki/Undersampling Of course, nowadays most often one just uses a very fast ADC, and one can then choose a suitable sub-band by decimation (in a FPGA or ASIC), a kind of digital frequency filtering. Undersampling was often used in older RF gear (and, maybe it still is for reaching the hightest frequencies? I don't know what's the current state of the art).
- ska 10y ago
  Note the "to avoid aliasing" in the comment you are responding to.
  - temac 10y ago
    You can also embrace aliasing if you are kind of crazy. Look for "compressed sensing" stuff. Although I'm unsure if this would be useful for anything on ultrasound systems.
    - ska 10y ago
      Compressed sensing really isn't the same thing - and to do it properly you need random sampling. Still it's interesting stuff !
  - ska 10y ago
    Not sure why downvotes. Parent is describing exactly the issues with undersampling that grandparent wanted to avoid.
- YZF 10y ago
  Yes. This is essentially like using a mixer in RF circuits. I'm pretty sure it's still used in many variations. Generally speaking you can't go high enough in sample rate to allow every RF signal (in the GHz possibly) to be sampled directly. It's always some sort of frequency shifting + filter. The key is to filter out frequencies out of the band before sampling and the band does not need to start from DC (0Hz).

by zild3d 10y ago

nickff 10y ago

Your actual sampling rate will be higher than the Nyquist if you are trying to process data from an array, as the sampling rate required to detect phase shifts depends on the sampling period (which is determined by how quickly you want to 'move' the array).

cnvogel 10y ago

This is not strictly true. You can reproduce a band-limited signal as long as the bandwidth of this signal is smaller than half the sampling frequency. For example, a signal that only has energy in the range of 9MHz to 11MHz has a center frequency of 10MHz, but a Bandwidth of 2 MHz. You could sample, and reconstruct, the signal perfectly with a sample-rate higher than 4 MHz. Any content between DC and 9MHz that would be present would distort the sampled waveform, though, and create artifacts. https://en.wikipedia.org/wiki/Undersampling https://en.wikipedia.org/wiki/Undersampling Of course, nowadays most often one just uses a very fast ADC, and one can then choose a suitable sub-band by decimation (in a FPGA or ASIC), a kind of digital frequency filtering. Undersampling was often used in older RF gear (and, maybe it still is for reaching the hightest frequencies? I don't know what's the current state of the art).

ska 10y ago
Note the "to avoid aliasing" in the comment you are responding to.
- temac 10y ago
  You can also embrace aliasing if you are kind of crazy. Look for "compressed sensing" stuff. Although I'm unsure if this would be useful for anything on ultrasound systems.
  - ska 10y ago
    Compressed sensing really isn't the same thing - and to do it properly you need random sampling. Still it's interesting stuff !
- ska 10y ago
  Not sure why downvotes. Parent is describing exactly the issues with undersampling that grandparent wanted to avoid.
YZF 10y ago
Yes. This is essentially like using a mixer in RF circuits. I'm pretty sure it's still used in many variations. Generally speaking you can't go high enough in sample rate to allow every RF signal (in the GHz possibly) to be sampled directly. It's always some sort of frequency shifting + filter. The key is to filter out frequencies out of the band before sampling and the band does not need to start from DC (0Hz).