Lecture Notes: Generating Exponential Trend Lines in MATLAB

Overview

• Focus on modeling the decay of brightness in a phosphorescent strontium aluminate compound using an exponential model.
• Data set includes:
  • t: Time points (hours) for brightness measurement.
  • LR: Relative brightness (current brightness / initial brightness).
  • At time zero: Relative brightness = 1.

Plotting the Data

• Initial Plot: Bare bones graph
  • No grid lines, labels, or rules.
• Axis Font Size Adjustment
  • Use AH.fontsize = 18 to resize font and adjust grid line spacing.

Adding Labels and Titles

• X Label: Time (hours)
  • Older method: Specifying font size within xlabel() function.
• Y Label (Relative Brightness)
  • New method: Assign a text object to a variable (e.g., yl = ylabel()), then use yl.fontsize = 16.
• Title
  • Assign text object to a variable (e.g., t = title()), then adjust properties.
  • Note: Title is bold by default, can be multiple lines using cell array.

Strontium Aluminate Compounds

• Generic term for compounds with strontium, aluminum, and oxygen.
• Different compounds based on element ratios.
• Fluorescence achieved by adding a dopant (e.g., europium or dysprosium).

Calculating Model Parameters

• Use polyfit() with log() of LR to fit data:
  • M: Extracted from first element.
  • B: Calculated as e raised to the second element.
• Create theoretical data set:
  • Use linspace() to generate equally spaced time values.
  • Ensure first and last elements match data points.

Plotting the Model

• Use hold on to plot the theoretical data on the same graph.
• Check trend line fit visually for accuracy.

Adding Trendline Equation

• Use sprintf() to format equation:
  • Insert B and M values with proper formatting for subscripts and superscripts.
  • Employ curly braces for superscripting.
• Place equation on the graph with the text() function:
  • Create a text object for further customization.
• Customization Options:
  • Adjust font size, color, background, and edge color using dot notation.

Conclusion

• Demonstrated the application of exponential models in MATLAB.
• Highlighted methods for customization and refinement of data visualization.
• Next steps: Transition to a new topic.