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Fourier Transform
Published in Kayvan Najarian, Robert Splinter, Biomedical Signal and Image Processing, 2016
Kayvan Najarian, Robert Splinter
Before discussing the main usage of the FT in linear systems, we briefly discuss the concept of linear systems that play an important role in signal and image processing. Consider a system where an “input” stimulation of the system causes an “output” response from the system. For example, consider a cart on an open area such a parking lot. If you push the cart with a certain input power, the cart will travel an output distance. Linear systems are the systems in which the output linearly depends on the input, i.e., the amplitude of the output is linearly proportional to the amplitude of the input. Using the example mentioned earlier, if one pushes a cart with twice the original force or power, the cart will travel twice the original distance. In a more mathematical context, if a push with power p(t) causes the cart to travel for q(t) meters, then a push for α·p(t) will cause the cart to travel for α·p(t) (where α is a constant).
Implementing Solutions
Published in James William Martin, Lean Six Sigma for the Office, 2021
Measurement systems need to be verified for accuracy and repeatability i.e. consistency and several other measures. These systems consist of environmental influences, measurement procedures, the types of measuring equipment, the types of manual intervention, and materials. Depending on what is being measured, there are six components of measurement error if people are making measurements using tools. The six measurement components are resolution, stability, linearity, accuracy, reproducibility, and repeatability. Automated systems do not have all six components. The resolution of a measurement system is its ability to detect changes in the variable being measured. As an example, to detect changes in distance of a meter with adequate resolution, distance needs to be measured in centimeters or millimeters. Or if a team needs to detect hourly changes in cycle time, then a time-stamp-based day would not have adequate resolution. The team would need to increase the measurement resolution by moving it to minutes. Resolution issues once recognized are the easiest measurement error to eliminate. Stability errors occur if a variable’s measured average value changes with respect to its true value over time. An example would be employee performance reviews or skills acquired through training that deteriorate if not periodically reinforced through subsequent training activities. Linearity is the ability of a measurement system to measure a variable with the same variation around its true value over the range of measurement. An example is when rating scales are skewed toward one end or another in customer satisfaction surveys.
Transducer
Published in Francis S. Tse, Ivan E. Morse, Measurement and Instrumentation in Engineering, 2018
Let us examine the implications of linearity in instruments. Linearity is desirable. It eliminates the bother of referring to a calibration chart or a conversion table, although this can be mechanized, such as by means of a microprocessor. A system with a nonlinear component is a nonlinear system, and the mathematical analysis is more difficult than that for linear systems. Fortunately, most systems can be linearized and their performances reasonably predictable by linear theory [7].Linearity simply means that the output is nominally proportional to the input. It does not imply better accuracy, higher precision, or greater sensitivity. For example, a household thermometer is nominally linear. It would be absurd to read the thermometer with a microscope and proclaim a ±0.01°C accuracy. In fact, the linear characteristic in Fig. 2-5d does not even pass through the origin of the coordinates.A nonlinear instrument can be accurate and even desired in some cases. For example, a high-quality voltmeter may have a logarithmic scale, which is nonlinear. Moreover, a log scale is linear in decibels (see Fig. 4-23), a unit used in sound-level measurements. Incidentally, a meter has proportional linearity if the uncertainty in the dial reading is a constant amount, say ±1 mm, and the dial has a logarithmic scale. The paradox is that proportional linearity is achieved by means of a nonlinear scale.
Analytical method development and percutaneous absorption of propylidene phthalide, a cosmetic ingredient
Published in Journal of Toxicology and Environmental Health, Part A, 2021
Ji-Young Kim, Jueng Eun Im, Jung Dae Lee, Kyu-Bong Kim
The developed method was validated in terms of selectivity, lowest limit of quantitation (LLOQ), linearity, stability, accuracy and precision according to the MFDS guidelines for validation of biological samples (MFDS 2013). Selectivity was confirmed by comparing the extracted blank skin, SC, SW, and receptor fluid samples with the LLOQ samples. To evaluate linearity, results from calibration standard analyses (60, 100, 200, 500, 1,000, 1,600, or 2,000 ng/ml) were placed into a calibration curve. The 1/x2 weighted factor was used for good calibration curve of the peak area ratio between PP and IS. The stability test was carried out for 24 hr. PP was diluted with methanol to 10 mg/ml, and then 50% ethanol added to a final concentration of 1 mg/ml. The solution was stored at 32°C in a shaded 1-ml syringe after removing air. The samples were collected in 200-μl portions at 0, 1, 2, 4, 8, 12, and 24 hr. The collected samples were analyzed through the aforementioned procedure. Accuracy (the closeness of the nominal value and measured value determined by the analytical method) and precision (the nearness between measured values of the sample, relative standard deviation) were evaluated through analysis of QC samples in inter- and intra-day. The MFDS guidelines for validation of biological samples recommends accuracy and precision to be assessed using 4 concentration levels for 3 days (4 concentrations with three replicate assessments each day). The 4 concentration levels of QC samples utilized for evaluating accuracy and precision were 60, 180, 600, and 1,800 ng/ml .
Pharmacokinetics and tissue distribution of an orally administered mucoadhesive chitosan-coated amphotericin B-Loaded nanostructured lipid carrier (NLC) in rats
Published in Journal of Biomaterials Science, Polymer Edition, 2020
Janet Sui Ling Tan, Clive Roberts, Nashiru Billa
Statistical evaluation on samples was performed using a one-way analysis of variance (ANOVA) followed by an independent t-test, where differences were considered significant when p < 0.05. Linearity was evaluated by linear regression analysis, which was calculated by least squares regression analysis and the ANOVA test. All calculations were conducted using IBM SPSS Statistics 24 (IBM cooperation, New York, NY).