2018-10-13

Lecture 4, Systematic errors and sampling

Additional strategies for mitigating systematic errors

4. Null method: e.g. current bridge. The indicating device does not need to be linear or even calibrated.

5. Watch out for changes in time: e.g. do "ABC ABC ABC" instead of "AAA BBB CCC" because the experiment result may drift in time.

6. Differential measurements: e.g. measure the temperature w.r.t a standard and similar to the desired temperature, for example, thermal couple output ~ 100C compared to the output in boiling water.
   whats the difference between this and the null method?

N.B. Always approach a measurement from the same side to avoid backlash.

7. Selection effects: make sure you are measuring the thing you want to measure. Avoid spurious correlation.

Digital Sampling

• Record instantaneous values of at regular intervals.

• Fourier Transforms

Examples: cos, sinc, comb !!!! should have produced accompanying graphs

• Minimum sampling rate: Nyquist Criterion basic version
  For a band-limited function, need to sample at a minimum rate of twice the highest frequency Fourier component present in the signal.
  If the sampling is noiseless, can recover the signal perfectly from its samples.

• Aliasing
  Present when the Nyquist criterion is not met.
  
  where
  
  also notice that it can only represent an aliasing of an aliasing if the original signal is too high.

• Convolution
  
  Convolution with the comb function (a series of delta function) leads to replication of the original function at each delta point.

• Convolution theorem

Convolution in one domain is proportional to point-wise product in the other domain.