Sentence examples for by writing the convolution from inspiring English sources

By writing the convolution as a matrix operation, a least squares (LS) estimate for h SI can be obtained, which we denote by (hat {h}_{text {SI}}).

Since (3.10) can be written in the convolution form (3.12).

On the other hand, we could have proceeded by writing equations (3) and (4) first as a convolution product on z and then perform a FT on the variable y (see Appendix/Fourier Transform).

The same set of rules leads to Note that we can exchange the order of integration on y and z, write the first integral as a convolution product on functions of z and proceed to the second integral by using the FT on y.

In "Snakeskin," for instance, Voigt writes: "The snail empties the endless / convolutions of its shell.

To obtain the breeder's equation of the previous section, we wrote the integration over the y variable as a convolution product and performed the FT on the z variable.

We denote by ∗ the convolution.

Here we denote by ∗ the convolution.

Notation Throughout the paper, we denote by ∗ the convolution.

Parts of the first term of the right-hand side are written as convolutions, by exploiting the along-strike invariance of the Green's function, and efficiently computed by the Fast Fourier Transform (e.g., Rice, 1993; Liu and Rice, 2005).

It is constructed by the convolution of exponential distribution.