What is sigma function?

Hi all, this is an assignment of from class digtal signal processing. The question 1 is the image "Question1", what is the sigma function? anyone knows please explain to me. How can I plot like the answer?

Answer 1

[Steven Lord]

From Wikipedia: "In general mathematics, uppercase Σ is used as an operator for summation." In MATLAB see the sum function.

I'm guessing you're fairly new to MATLAB, am I right? If so you might want to go through the free MATLAB Onramp tutorial (https://www.mathworks.com/support/learn-with-matlab-tutorials.html) to quickly learn the essentials of MATLAB. It should take about 2 hours according to the webpage (I haven't actually gone through it myself.)

[Walter Roberson]

Also note that δ is not sigma, which would be written as σ . Instead δ represents the Dirac Delta. In that context, δ is a function that is 0 whenever its input is non-zero, and is 1 when the input is exactly 0.

δ(x) = (x==0)

so for example δ(x-3) would be 0 for all x except when x==3 exactly in which case it is 1.