Data Sampling Rates

In order to reduce the size of data files, there is usually a software function that permits the selection of either the number of data points to be collected or a specific 

Curves Offset to Equivalent Heat Flow Baseline 

FIGURE 2.10 Effect of heating rate on the DSC data for 2.78 mg of indium in an aluminum general pan. Nitrogen purge gas at 25 ml/min. 

Effect of Changing the Heating Rate on the Transition Values for Indium Measured by DSC 

Heating Temperature Enthalpy Temperature Height Half Height Time 

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The value of fEdetermines all other variables in the equations above. In turn, fE is determined by the temporal resolution of interest of the system studied. To resolve an average excited state lifetime t, the required data sampling rate, in frequency domain techniques is at least an order ofmagnitude slower than it is in the time domain as stated by the following relation (when Np > 32 and Nw= 1) ... 

Improve S/N ratio of peaks to >50 if possible and use a data sampling rate of >8 points/peak. 

The data sampling rate of the analog to digital (A/D) converter ... 

The Effect That Changing the Data Sampling Rate Has upon the Measured Values for the Melting of Indium... 

Figure 3.17. TG curves of CaCjO H20 as repfotted on a data center recorder (59). Heating rate of 10°C min"1 in N3. Data sampling rate was 1.0 sec. A, Mass-time, scaled and offset B, mass-temperature, scaled and offset C, mass-time D, mass-temperature E, first derivative-temperature F, temperature-time.

MP3 files contain audio that is digitally encoded using an algorithm that compresses the data by a factor of about eleven but yields a reasonably faithful reproduction. The quahty of sound reproduced depends on the data sampling rate, the quality of the encoder, and the complexity of the signal. 

Figure 17.2.3 (A) Curve 1 Tip current with time for a solution of 2 mM CpjFeTMA and 2.0 M NaNOj with a Pt-Ir tip at 0.55 V vs. SCE and an ITO substrate at —0.3 V d 10 nm. Curve 2 Time series of the tip current for d within the tunneling range in a solution containing only 2.0 M NaNOj tip radius 7 nm. Data sampling rate was 0.4 sec per point. (B) Corresponding time correlation function. (C) Probability density function of time series 1 in (A). Adapted with permission from reference (8).

Figure 17.2.4 Time evolution of the tip current observed at a tip potential = 0.6 V and a n-TiOj substrate potential = —0.7 V (curve 1) or 0.0 V (curve 2) vs. SCE for various distances in a solution containing 2 mM CpjFeTMA and 1.0 M NaNOj. The data sampling rate was 0.4 sec per point. (A) With tip far away from the substrate (B) d 13 run, which gave an average steady-state current of -7.6 pA when E = —0.7 V vs. SCE (C) rf - 11 nm, which gave an average steady-state tip current of -6.1 pA. Adapted with permission from reference (8).

The main quantities of interest, namely, temperature, time, and heat flow rate, must be measured and stored for later evaluation. The data sampling rate must be chosen properly not to get too Uttle or too much data for the event in question. Of course, the analog-to-digital converter must have the proper resolution and precision to fidflll the uncertainty demands of the measurement. 

This chapter consists of six sections. Section 4.2 introduces the FSF model structure. Section 4.3 examines the properties of the FSF model with a fast data sampling rate. Section 4.4 introduces the concept of a reduced order FSF model. Section 4.5 discusses the use of least squares for estimating the FSF model parameters from input-output data. Section 4.6 excunines the nature of the correlation matrix that arises when using a least squares estimator with an FSF model and the relationship between the elements of this matrix and the energy content of the input signal. 

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