NumPy: The Core of Numerical Computing

Final Project: Multidimensional Analysis and Vectorized Signal Processing

This final project requires you to build a comprehensive numerical analysis pipeline using NumPy. You will simulate and process complex sensor data to demonstrate your mastery of array manipulation and performance optimization. Tasks include: 1. Data Synthesis: Create a 3D NumPy array (shape: 1000, 10, 5) representing time-series data for 10 sensors across 5 different experimental conditions using a combination of normal and uniform distributions. 2. Preprocessing: Utilize boolean indexing and masking to identify and replace simulated missing values (NaNs) and apply a Min-Max normalization across the temporal axis for each sensor. 3. Statistical Analysis: Calculate the mean, standard deviation, and peak-to-peak values for each sensor-condition pair using specified axis parameters. 4. Linear Algebra: Compute the correlation matrix for the sensors and derive the principal components of the data using np.linalg.eig to understand sensor dependencies. 5. Performance Optimization: Implement a custom signal smoothing function (moving average) using NumPy's broadcasting or stride tricks and provide a benchmark comparison against a standard Python for-loop implementation. Your final submission must be a Jupyter Notebook or a clean Python script including inline documentation.