Causal (Periodic) Signals

A signal $x\in{\bf C}^N$ may be defined as causal when $x(n)=0$ for all ``negative-time'' samples (e.g., for $n=-1,-2,\dots,-N/2$ when $N$ is even). Thus, the signal $x=[1,2,3,0,0]\in{\bf R}^5$ is causal while $x=[1,2,3,4,0]$ is not. For causal signals, zero-padding is equivalent to simply appending zeros to the original signal. For example,

$$\hbox{\sc ZeroPad}_{10}([1,2,3,0,0]) = [1,2,3,0,0,0,0,0,0,0].$$

Therefore, when we simply append zeros to the end of signal, we call it causal zero padding.