Let us write a convolution(adsbygoogle = window.adsbygoogle || []).push({});

$$\int_{0}^{t} A(t-\tau) \mathrm{d}x(\tau)$$ as

$$A \star \mathrm{d}x$$

I would like to write down the expression for the double convolution

$$A \star \mathrm{d}x \star \mathrm{d}x $$

Following the definition I obtain

$$ \int_{0}^{t} \int_{0} ^{t-\tau} A(t-\tau-s) \mathrm{d}x(s) \mathrm{d}x(\tau)$$

Can this be given a more compact form, especially in reference to the upper limit of integration in the inner integral?

I would like to perform the change of variable $$t-\tau = w$$ but unsure as to how to proceed, any hint would be the most appreciated, thanks

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Double Convolution

Loading...

Similar Threads - Double Convolution | Date |
---|---|

A Maximization Problem | Jan 31, 2018 |

I Q about finding area with double/volume with triple integral | Sep 13, 2017 |

B Derivative with the double cross product | Jul 18, 2017 |

I Find total charge (using double integration) | Apr 15, 2017 |

I Differentiability of convolution | May 23, 2016 |

**Physics Forums - The Fusion of Science and Community**