The TD_CONVOLVE function performs a two-dimension convolution operation, convolving the first source with the second one. Two-dimensional convolution is a mathematical operation that takes two input functions and produces an output function. It can be expressed as the integral of the product of two functions over all possible translations of one of the functions.
As in the case of the one-dimension convolve, the convolve operation is often referred to as a filtering operation. The filter matrix to be applied is often referred to as a point spread function. A practical application of TD_CONVOLVE2 is the use of a filter on a two-dimensional pixelated image.
The filter is a small matrix that moves across the image, and at each location, the convolution operation multiplies the values in the filter with the corresponding pixel values in the image and sums up the results. This sum is then placed at the output position corresponding to the center of the filter, and the process is repeated until the entire image has been processed.
Images can be sharpened, blurred or undergo a filtering transformation that identifies edges in the image. Smaller images that produce result matrixes smaller than 128 by 128 use a summation approach. Larger images use a Discrete Fast Fourier Transform (DFFT) method.
Two-dimensional convolution is also applied to time series data, where the input is a one-dimensional signal instead of a two-dimensional image. The time series is treated as a two-dimensional matrix, where one axis represents time, and the other axis represents a particular feature or variable.
The process of two-dimensional convolution for time series is similar to that for images. A small matrix or filter moves along the time axis of the signal. The use of two-dimensional convolution for time series analysis is useful for feature extraction, denoising, and trend analysis. By applying different kernels, different features of the time series are extracted or enhanced, providing insights into the underlying patterns and trends.