*Question E8A01:
What technique shows that a square wave is made up of a sine wave and its odd harmonics?*  

*Correct Answer is  A: Fourier analysis*  

### AI Response: (may contain errors)  

The correct answer to the question is **A: Fourier analysis**. 

### Explanation:

1. **Why Fourier analysis is correct:**
   - Fourier analysis is a mathematical technique that decomposes a periodic function (like a square wave) into a sum of sine and cosine functions. 
   - A square wave can be represented as a series of its fundamental frequency and its odd harmonics (3rd, 5th, etc.). This is known as the Fourier series representation.
   - The formula for a square wave can be expressed as:
     $$
     f(t) = \frac{4}{\pi} \sum_{n=1,3,5,\ldots}^{\infty} \frac{1}{n} \sin\left(2\pi nt/T\right)
     $$
     where $T$ is the period of the square wave.

2. **Why the other choices are incorrect:**
   - **B: Vector analysis**: This is a branch of mathematics that deals with vector fields and does not apply to the decomposition of waveforms.
   - **C: Numerical analysis**: This involves algorithms for approximating solutions to mathematical problems and is not specifically focused on waveforms or their harmonic content.
   - **D: Differential analysis**: This is concerned with the study of rates of change and derivatives, which does not directly relate to the harmonic composition of waveforms.

### Summary:
- **Fourier analysis** is the correct technique for showing that a square wave consists of a sine wave and its odd harmonics.
- The other options do not pertain to the analysis of waveforms in the same way. 

This understanding is crucial for grasping how different waveforms can be synthesized and analyzed in amateur radio and signal processing.