Explanation of the need to understand basic principles before diving into signal processing algorithms.
The beauty of mathematics and its role in digital signal processing.
Overview of the types of oscillations in nature.
Introduction to the laboratory setup.
Personal experience and motivation for learning math analysis.
Explanation of the graphs and coordinate systems used in the presentation.
Slide2: Fourier Transform
Explanation of how Fourier transform is essential in digital signal processing.
Introducing the concept of complex plane and its representation of complex numbers.
Visual representation of the amplitude of oscillations on a graph.
Demonstration of the transformation process using a rotating line on the complex plane.
Relating the length of the line on the complex plane to the amplitude of the signal.
Slide3: Frequency Analysis
Explanation of how frequency analysis helps understand the periodicity of a signal.
Finding the period of oscillation and calculating the frequency.
Demonstration of the movement of the center of mass on the complex plane.
Relating the position of the center of mass to the number of oscillation cycles.
Observing the behavior of the signal as the frequency of rotation matches the signal frequency.
Slide4: Zero Frequency
Exploring the significance of zero frequency in signal rotation.
Demonstrating the representation of zero frequency on the complex plane.
Visualizing the behavior of the signal when the frequency of rotation is zero.
Understanding the influence of negative signal values on the rotation.
Observing the change in the shape of the signal when the frequency of rotation matches the signal frequency.
Slide5: Multiple Frequencies
Exploring the decomposition of a signal with multiple frequencies.
Demonstration of a signal with two different frequencies.
Observation of the decomposition process and extraction of individual components.
Incorporation of an additional frequency component in the signal.
Confirmation of the successful decomposition of multiple frequencies.
Slide6: Fourier Transform Formula
Introduction to the mathematical formulas for the Fourier transform.
Deriving the discrete Fourier transform formula.
Relating the rotation of the complex plane to the functions representing the horizontal and vertical coordinates.
Conversion of the discrete formula to the integral form.
Comparison to the classical definition of the Fourier transform.
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