## Impulse Response of discrete system

Impulse signal can be represented as:d[n] = 1, if n=0d[n] = 0, otherwiseit can also be written like d=[1,0,0,0,â€¦] Impulse Response The impulse response h(n) is the response of filter L() at time n to unit impulse occurring at time 0.h(n)=L(d(n))Let’s see how a discrete system can be described when impulse response is known We know that: In the linear system this can be written as follows: Because h(n-k)=L(d(n-k))Then: What do we get? Its impulse response can describe a linear system. The last expression is called convolution. This is the heart of DSP Filtering.To write this sum in the more convenient matter is assumed that: Matlab example Matlab example: As you can see if the input queue has N samples, impulse response has M after convolution there will be total N+M-1 samples.