Coefficients as Impulse Response

• If we look at the response of the filter to an impulse

  >> x(1:10)
  
  ans = 
  
       1 0 0 0 0 0 0 0 0 0
  
  >> y(1:10)
  
  ans = 
  
       1 1 0 0 0 0 0 0 0 0
  

  we see the impulse response $y$ is equivalent to coefficients of our FIR filter.

• This can be expressed using the general FIR equation, with an input of $x(n) = \delta(n)$:
  $$h(n) = \sum_{k=0}^Mb_k\delta(n-k) = b_n.$$