Document ID: chunk:federal_register_of_legislation:F2017L01221:body:0:p14
Version: federal_register_of_legislation:F2017L01221
Segment Type: other
Provision Reference: 
Character Range: 37050–39774

stop bands and the attenuation and allowable ripple in each; and correction of filter phase lags. Each of these factors shall be considered in order to achieve a relative overall data acquisition accuracy of ±0.5 per cent.
2.2. Aliasing errors
 In order to avoid uncorrectable aliasing errors, the analogue signals shall be appropriately filtered before sampling and digitizing. The order of the filters used and their pass band shall be chosen according to both the required flatness in the relevant frequency range and the sampling rate.
 The minimum filter characteristics and sampling rate shall be such that:
(a) Within the relevant frequency range of 0 Hz to fmax = 30 Hz the attenuation is less than the resolution of the data acquisition system; and
(b) At one-half the sampling rate (i.e. the Nyquist or "folding" frequency) the magnitudes of all frequency components of signal and noise are reduced to less than the system resolution.
 For 0.05 per cent resolution the filter attenuation shall be less than 0.05 per cent in the frequency range between 0 and 30 Hz, and the attenuation shall be greater than 99.95 per cent at all frequencies greater than one-half the sampling frequency.
 Note: For a Butterworth filter the attenuation is given by:

           where:
  n is the order to filter;
  fmax is the relevant frequency range (30 Hz);
  fo is the filter cut-off frequency;
  fN is the Nyquist or "folding" frequency.
  For a fourth order filter
  for A = 0.9995: fo = 2.37 ∙ fmax
  for A = 0.0005: fS, = 2 ∙ (6.69 ∙ fo), where fS, is the sampling
frequency = 2 ∙ fN.
2.3. Filter phase shifts and time delays for anti-aliasing filtering
 Excessive analogue filtering shall be avoided, and all filters shall have sufficiently similar phase characteristics to ensure that time delay differences are within the required accuracy for the time measurement. Phase shifts are especially significant when measured variables are multiplied together to form new variables, because while amplitudes multiply, phase shifts and associated time delays add. Phase shifts and time delays are reduced by increasing fo. Whenever equations describing the pre-sampling filters are known, it is practical to remove their phase shifts and time delays by simple algorithms performed in the frequency domain.
 Note: In the frequency range in which the filter amplitude characteristics remain flat, the phase shift Φ of a Butterworth filter can be approximated by
  Φ = 81 ∙ (f/f0) degrees for second order
  Φ = 150 ∙ (f/f0) degrees for fourth order
  Φ = 294 ∙ (f/f0) degrees for eighth order
  The time delay for all filter orders is: t = (Φ/360) ∙ (1/f0)
2.4. Data sampling and digitizing
 At 30 Hz the signal amplitude changes