Understanding Convolution in IDL: Smoothing and Kernel Length Explained

[big man]

I'm having a bit of trouble with this since the one page lecture note on this doesn't explain much and I can't really find any useful resources on the net.

I understand that convolving a function can be like smoothing the function using a moving average, but then I don't see how you would make your kernel artificially long in IDL when you have a large array that you are wanting to convolve with the kernel.

Let's say we have an array as follows:

Array = fltarr(4000)

I want to do a 48 month centred moving average. If you look through the time series array then let's say that you see the data covers 10 blocks of 48 months. Would you then have a kernel that has 10 central values of 1/10 with a whole heap of 0s either side?

eg Kernel = [...0,0,1/10,1/10...,0,0...]

If that is the case then how do I do this for an array of 4000 elements. I mean there must be a way were you can define what you want your central values of the kernal to be and then have IDL automatically make it a 4010 element array with 0s filling the rest of the array.

IDL gives the notation of convolution as follows:

Convol(array, kernel, scale factor)

However, the help says that the kernel has to be smaller than the Array, but my lecture notes say that you have to make the kernel artificially long otherwise IDL doesn't allow you to run the kernel through the function properly.

I'd greatly appreciate any help at all

 

[nate808]

Thank you for sharing your difficulties with convolving a function. I can understand how confusing it can be when there is limited information available on a topic. I will try my best to provide you with some guidance on this matter.

Firstly, let me clarify that convolving a function is a mathematical operation that combines two functions to create a third function. In your case, you are trying to convolve a function (the array) with a kernel (a smaller function) to create a smoothed version of the original function. This can be done by using the convolution function in IDL, as you have mentioned.

Now, to address your specific concern about making the kernel artificially long, I would suggest using the "convolution theorem" which states that convolution in the time domain is equivalent to multiplication in the frequency domain. In simpler terms, you can create a longer kernel by padding zeros to the original kernel, which will have the same effect as convolving with a longer kernel.

In your example, you can create a kernel of length 480 (48 months x 10 blocks) and pad it with 3520 zeros to make it a 4000 element array. This will give you the desired result of a 48-month centered moving average.

I hope this helps in solving your problem. If you need further clarification or assistance, please do not hesitate to ask. As scientists, we are always happy to help and support each other in our research endeavors. Keep up the good work!

 

[Architeuthis Dux]

.

I understand your confusion with the concept of convolution in IDL. Let me try to explain it in simpler terms.

Convolution is a mathematical operation that combines two functions to produce a third function. In the case of smoothing, the first function is the data array and the second function is the kernel. The kernel acts as a weighted average that smooths out the data points.

To make the kernel artificially long, you can use the "replicate" function in IDL. This function allows you to repeat the central value of the kernel multiple times, creating a longer kernel with zeros on either side. For example, if you want a 48-month centered moving average, you can create a kernel of length 97 (48 central values repeated twice with zeros on either side).

As for the notation in IDL, the kernel does not necessarily have to be smaller than the array. It just has to be smaller than the array in the dimension that you are convolving. For example, if you have a 4000-element array and you want to convolve it along the time dimension, then your kernel can be of length 97 (as discussed above).

I hope this explanation helps you understand convolution in IDL better. If you are still having trouble, I suggest reaching out to your instructor or a colleague for further clarification. Additionally, there are many online resources and tutorials available that can provide more in-depth explanations and examples of convolution in IDL.