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

• snatchingthepi
In summary, the speaker is confused about a question that asks for the 1D convolution of a 2-dimensional function. They are unsure if they should ignore the "y" variable and only convolve with respect to "x", or if they are missing something. They also mention not having access to the required textbook and ask for the name of a function. Another person suggests doing two separate convolutions, one with respect to "x" and one with respect to "y". The speaker then explains how the equation can be written as two 1D convolutions.
snatchingthepi
Homework Statement
Evaluate and sketch the 1-D convolutions:
Relevant Equations
tri(x,y) ** (step(x) * 1(y))

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.

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).

Last edited:
snatchingthepi and berkeman
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))

berkeman

## 1. What is convolution?

Convolution is a mathematical operation that combines two functions to create a third function. It is commonly used in scientific fields such as signal processing and image analysis.

## 2. What does "tri(x,y)" mean in the equation?

"tri(x,y)" represents a triangular function, which is a type of function that has a triangular shape when graphed. It is often used in convolution operations as a smoothing function.

## 3. What is the significance of "(step(x) * 1(y))" in the equation?

"(step(x) * 1(y))" represents a step function, which is a function that changes abruptly from one constant value to another. In convolution, this function is used to define the boundaries of the convolution operation.

## 4. How does convolution help in scientific research?

Convolution is a useful tool in scientific research as it allows for the analysis and manipulation of data, particularly in signal processing and image analysis. It can help to identify patterns and relationships between different sets of data.

## 5. Are there any limitations to convolution in scientific research?

While convolution is a powerful tool, it does have some limitations. It is most effective when used on linear, time-invariant systems and may not be suitable for more complex systems. Additionally, the accuracy of convolution results can be affected by noise in the data.

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