Signal and Transform

Syllabus

1. Fundamentals of Signal Processing in Geomatics (7 hours)
   1. Signals and systems: Understanding signals (Spatial data) and systems used in processing them
   2. Signal representation: Techniques for representing spatial signals, such as elevation and spectral data
   3. Sampling and quantization: Methods for converting continuous geospatial data into digital formats
   4. Basic signal operations: Operations such as addition and scaling applied to spatial datasets
2. Fourier Transform for Geospatial Analysis (7 hours)
   1. Fourier series and transform: Decomposition of spatial signals into frequency components for feature analysis
   2. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT): Frequency analysis methods for raster data and satellite imagery
   3. Spectral analysis: Identifying frequency patterns in geospatial data for classification tasks
   4. Fourier in image processing: Enhancing and processing images using Fourier techniques
3. Digital Filtering Techniques for Spatial Data (7 hours)
   1. Digital filters overview: Types of filters (low-pass, high-pass) used in spatial data enhancement
   2. Filter design: Creating filters to remove noise and highlight features in geospatial datasets
   3. Filter performance analysis: Evaluating the effectiveness of filters in improving data quality
   4. Applications in geomatics: Practical use of filters for edge detection and smoothing in spatial data
4. Wavelet Transform and Multiresolution Analysis (8 hours)
   1. Wavelet transform basics: Introduction to wavelets and their application in analyzing spatial data at different scales
   2. Discrete wavelet transform (DWT): Techniques for multiresolution analysis of high-resolution satellite images
   3. Wavelet-based image processing: Enhancing features and compressing images using wavelets
   4. Multiresolution analysis: Improving the interpretation of spatial phenomena by analyzing data at various scales
5. Time-Frequency Analysis for Geospatial Data (8 hours)
   1. Time-frequency representations: Analyzing geospatial data with varying features over time
   2. Short-time Fourier transform (STFT): Handling non-stationary spatial signals for temporal analysis
   3. Spectrogram analysis: Visualizing frequency changes in time-series geospatial data
   4. Remote sensing applications: Analyzing time-series data from remote sensing platforms
6. Advanced Signal Processing Techniques (8 hours)
   1. Adaptive filtering: Dynamic filters adjusting to changing characteristics in geospatial data
   2. Principal component analysis (PCA): Reducing dimensionality and extracting key features from spatial data
   3. Time-series analysis: Modeling and analyzing temporal changes in geospatial datasets
   4. Signal reconstruction: Techniques for interpolating and enhancing missing or degraded data

Practicals

1. Hands-on practice with fundamental operations on geospatial signals
2. Analyzing spatial data using Fourier techniques
3. Design and Test Digital Filters: Developing and applying filters to enhance spatial data
4. Enhancing and analyzing satellite images with wavelet techniques
5. Analyzing time-series data for dynamic geospatial changes
6. Implementing PCA and adaptive filtering in real-world scenarios