Complete Implementation of Deconvolution Operations

Deconvolution is a crucial signal processing technique primarily used to eliminate system effects on signals or restore original signals. Unlike directly calling pre-built library functions, manual implementation of deconvolution reveals its mathematical essence and computational process more clearly, demonstrating core algorithmic logic through step-by-step code execution.

The fundamental approach consists of three key phases: First, constructing the system's impulse response model, which serves as the core foundation for deconvolution. This can be implemented using array operations to represent discrete impulse response sequences. Second, converting time-domain problems to frequency domain processing through Fourier Transform (utilizing FFT algorithms), where theoretical deconvolution is achieved via division operations in the frequency domain - implemented using element-wise array division. Finally, addressing noise suppression issues where methods like Wiener filtering can be introduced at this stage, incorporating noise power spectrum estimation in the implementation.

Regarding implementation details, special attention must be paid to handling truncation errors caused by discrete sampling and numerical instability due to ill-conditioned systems. Regularization techniques (such as Tikhonov regularization) can significantly improve result robustness, implemented by adding small constants to denominators during frequency division. The entire process fully embodies the sophisticated integration of signal processing theory and numerical computation, providing excellent educational value for understanding linear system characteristics through practical code implementation.