Convolution Help on tri(x,y) ** (step(x) * 1(y))

[snatchingthepi]

Homework Statement

Evaluate and sketch the 1-D convolutions:

Relevant Equations

tri(x,y) ** (step(x) * 1(y))

I have some confusion about this question.

I am asked to do the 1D convolution of a function that is clearly 2-dimensional

tri(x,y) ** (step(x) * 1(y)) where ** is the convolution.

Furthermore my professor is not available for questions (have tried). I'm wondering if I simply ignore the bits of 'y' and convolve

tri(x) ** step(x)

or if there's something I'm missing. I don't have the text yet (on order - Easton's "Fourier Methods in Imaging") and the library doesn't have a copy either. Also if anyone happens to know the name of the function 1(y) I'd be most grateful.

 

[Delta2]

I think the exercise means to do two different convolutions, one with respect to x and one with respect to y.(it says evaluate and sketch the 1-D convolutions).
So first calculate the integral
$\int tri(t,y)step(x-t)1(y)dt$ (y is effectively a constant for this calculation) and then the integral $\int tri(x,t)step(x)1(y-t)dt$ (now x is considered to be a constant).

 

[snatchingthepi]

I found out what is going on. Turns out that since tri(x,y) => tri(x) * tri(y) the equation is separable and can be written as two 1d convolutions like

(f(x) ** h(x)) * (f(y) ** h(y))