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I often see a trick for calculating convolution of discrete data by a so-called Tabular method. There are a lot of Youtube videos and many Indian textbooks on Signal Processing [Books].1

Basically, if we have two series P = [1 3 5 3 1] and Q is [ 0 0 0 0.5 0.8 1 1 0 0 0]. One can make a table and multiply elements and sum up the diagonals as illustrated below. I color coded the diagonals. This process results in correct number of elements 10+5-1=14 elements.

Does anyone know who came up with this short cut? It seems like a nice approach for calculating convolution, correlation, cross correlation of discrete data.

Thanks.

Tabular method

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This reference claims to have invented the tabular method as a "novel method":

A novel method for calculating the convolution sum of two finite length sequences, J.W. Pierre (1996).

Three variations of the tabular method are discussed in The use of spreadsheets to calculate the convolution sum of two finite sequences (2004), citing a 1990 text book.

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  • $\begingroup$ Thank you for the first reference on 1990. It is very nice. The 2004 reference shows the same approaches as I did in Excel with color coding but he cites reference 11, which is another South Asian author's textbook. I am sure, this approach must be older than 1990s. Also it seems this tabular of approach is quite popular in Indian engineering schools (as deduced from Youtube videos). $\endgroup$ – M. Farooq Feb 20 at 16:57
  • $\begingroup$ indeed, added the link to the text book. $\endgroup$ – Carlo Beenakker Feb 20 at 21:13

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