Why Read This Book

You will get a rigorous, mathematically grounded treatment of multidimensional (N‑D) signal processing that stays relevant for image, radar, audio and communications applications. You will learn the fundamental N‑D transforms, sampling and interpolation theory, and practical filter‑design and spectral‑analysis techniques that make this a lasting reference for research and engineering.

Who Will Benefit

Graduate students, researchers, and practicing engineers with a solid 1‑D DSP background who need a deep, theoretical foundation and practical methods for designing and analyzing multidimensional signal‑processing systems.

Level: Advanced — Prerequisites: Undergraduate calculus and linear algebra, signals and linear systems (1‑D DSP fundamentals), Fourier transforms/DTFT, and comfort with complex variables and matrix methods.

Key Takeaways

• Apply the multidimensional z‑transform and DTFT to analyze N‑D linear systems and their frequency behavior.
• Design separable and nonseparable N‑D FIR filters using frequency‑sampling, windowing, and least‑squares approaches.
• Determine stability, causality, and region‑of‑convergence issues unique to multidimensional IIR systems and factorization limits.
• Perform sampling and reconstruction analyses in multiple dimensions and manage aliasing and anti‑aliasing constraints.
• Implement and reason about multidimensional DFT/FFT algorithms and computational strategies for N‑D spectral analysis.
• Translate theory to applications in image processing, radar, and communications by linking spectral properties to practical system design.

Topics Covered

1. 1. Introduction and Motivation for Multidimensional DSP
2. 2. Mathematical Preliminaries and Notation
3. 3. Multidimensional Fourier Transforms and the DTFT
4. 4. The Multidimensional z‑Transform and Regions of Convergence
5. 5. Convolution, Correlation, and Linear Shift‑Invariant N‑D Systems
6. 6. Sampling, Interpolation, and Reconstruction in Multiple Dimensions
7. 7. Spectral Analysis and Estimation for N‑D Signals
8. 8. FIR Filter Design: Separable and Nonseparable Methods
9. 9. IIR Filters, Stability, and Factorization in Multiple Dimensions
10. 10. Least‑Squares and Optimization Methods for N‑D Filter Design
11. 11. Computational Issues and Multidimensional FFT Algorithms
12. 12. Applications: Image, Radar, and Communications Examples
13. 13. Appendices: Supporting Mathematical Results

How It Compares

More focused on rigorous N‑D theory than Oppenheim & Schafer's Discrete‑Time Signal Processing (which emphasizes 1‑D fundamentals), and more mathematical than Gonzalez & Woods' Digital Image Processing, which is application‑oriented.