how should I stem convolution?

can anyone help me draw this convolution?

y[n] = dirac[n-1] * (U[n] - U[n-6])

I'm very new to matlab and I need some help to figure out my problem. tnx in advance...

[Walter Roberson]

What is dirac[n-1] intended to mean?

Is U a continuous function that is being sampled at integer locations? Or is it an array that is being indexed? If it is an array then y[1] through y[6] are not defined.

[Armin Javidfar]

this is the question

Answer 1

[Walter Roberson]

Under a quite reasonable interpretation of dirac[n-1], the function y[n] would always be 0 . Unless U can assume infinite values, in which case y would be undefined.

[Image Analyst]

You can convolve with delta functions. It's done all the time. Basically it makes replicates of things. Like the Fourier Transform of a rectangular aperture is a 2D sinc function and so the Fourier transform of 2D array of square holes (one hole convolved with a 2D comb function) is an array of 2D sinc functions (a signle sinc convolved with a 2D comb).

Answer 2

[Image Analyst]

Hint to get the difference of the U's

kernel = ones(1, 13);
kernel(7) = 1;
kernel(end) = -1;
du = conv(U, kernel, 'full');

[Walter Roberson]

However, the dirac[n-1] can be interpreted as only selecting this output if you are at the timestep before the current one, and since you never are, the answer has to come out 0. Jam yesterday and jam tomorrow but never jam today.

[Image Analyst]

n is not necessarily time. It could be space, and it's possible to sample (replicate) a location to the left of where you are. This dirac delta function and convolution stuff is used very extensively in Fourier optics regarding diffraction patterns.

[Walter Roberson]

It has to be time in this context. If you were sampling in space you would need to refer to the content of the location not just the index. For example, delta(X[n-1])

[Image Analyst]

I don't follow. n could be an index representing a location in time with units of seconds, or an index representing a location in space with units of mm or whatever. I believe convolution by the dirac delta simply shifts the difference of U's signal one index to the left. I wonder where this equation came from. Maybe it's a 1-D spatial masking situation, or if it's a time signal maybe it's some kind of feedback reduction/echo cancellation filter.