Definition | Model | |
---|---|---|
Signals | Are transformed by Systems into other Signals. | Can be modeled as Column Vectors. |
Systems | Transform Signals into other Signals. | Can be modeled as Matrices or Operators. |
Signals | Definition | Model |
---|---|---|
Continuous-Time (CT) | Domain and range is continuous. | Functions OR Real Valued Continuous Column Vectors. |
Discrete-Time (DT) | Domain is discrete, but range is continuous. | Real Valued Column Vectors. |
Digital Signals | Domain and range is discrete. | Rational Valued Column Vectors. |
Output | |||
---|---|---|---|
Discrete | Continuous | ||
Input | Discrete | Digital | DT |
Continuous | CT |
Memoryless | Causal | Noncausal | |
u(t< t_{0}) | No | Maybe | Maybe |
u(t=t_{0}) | Maybe | Maybe | Maybe |
u(t>t_{0}) | No | No | Yes |
Causal : u(t≤0) | Non-Causal : u(t) | |
Memoryless : u(0) | u(0) AND | u(t≥0) AND |
u(t<0) OR | ||
Distributed System : Infinite number of S.V. | Lumped System : Finite number of S.V. |
x_{1}(t) + x_{2}(t)} |
u_{1}(t) + u_{2}(t)} |
αx_{1}(t)} |
αu_{1}(t)} |
Input\Output | DT | CT |
DT | DFT or FFT | DTFT |
CT | Fourier Series | Fourier Transform |