Signals and Systems

7.1 CONVOLUTION THEOREM FOR CONTINUOUS SYSTEM

If the impulse response of an analog or continuous time system be h(t), it means that for an input δ (t) its output is h (t). Hence for linear system its output for a shifted impulse δ (t –T) is h (t –T). The following are the mathematical representation of these operations:

 

δ(t) h(t)

δ (t −T) h (t – T)

x(t) δ (t − T) x(T)h(t − T)

Obviously,      

From last two statements, we can say that for an ...