MATLAB Code Implementation of Sinc Interpolation

Sinc interpolation is a widely used method in digital signal processing, primarily employed for reconstructing continuous signals from discrete samples. Its core principle leverages the characteristics of an ideal low-pass filter, achieving distortion-free signal reconstruction through convolution operations with the sinc function.

Implementing sinc interpolation in MATLAB typically involves the following key steps:

Determining Original Sampling Points and Target Interpolation Positions Original signals are usually represented by sampled values at discrete time points. Interpolation requires clarifying the positional relationship between original sampling points and target interpolation points, such as whether additional points need to be inserted between existing samples. In MATLAB, this typically involves defining original time indices (e.g., t_original = 1:N) and target indices (t_target = 1:0.5:N for 2x interpolation).

Constructing the Sinc Function Kernel The sinc function is defined as sin(πx)/(πx). For interpolation, an appropriate sinc kernel must be constructed based on the sampling interval. Each interpolated point's value is calculated as the weighted sum of original samples with shifted sinc functions. In code, this can be implemented using: sinc_kernel = @(x) sin(pi*x)./(pi*x); with proper handling of the singularity at x=0.

Boundary Handling Practical applications involve finite-length signals, requiring careful boundary effect management. Common approaches include zero-padding, periodic extension, or symmetric extension to prevent distortion at signal boundaries. MATLAB implementations often use padarray() function or custom padding routines before convolution operations.

Calculating Interpolation Results For each target interpolation point, compute the weighted sum of sinc functions with all original sampling points. This can be implemented through matrix operations or loops, but vectorized operations in MATLAB significantly improve efficiency. The interpolation can be expressed as: y_interp = sum(y_original .* sinc((t_target - t_original)/T), where T is the sampling period.

Performance Optimization Due to the slow decay of sinc functions, practical implementations typically require windowing (e.g., Hamming window) to reduce computational load and suppress Gibbs phenomenon. For large datasets, frequency-domain implementation using FFT (via interpft function) may offer higher efficiency. MATLAB's vectorization capabilities and built-in functions like interpft facilitate efficient interpolation implementations.

Sinc interpolation finds important applications in signal reconstruction and image super-resolution, though its computational complexity requires careful balance between accuracy and real-time performance. MATLAB's vectorized operations and built-in functions provide effective tools for implementing high-quality interpolation.