13.4 : 偶数信号と奇数信号

An even signal, either in continuous-time or discrete-time, is defined as a signal that matches its own time-reversed version.

Even signals are symmetrical around the vertical axis, meaning that the signal for negative time values mirrors the signal for positive time values.

A signal is termed odd if it equates to the negative of its time-reversed counterpart.

Odd signals are recognized by their antisymmetrical nature about the vertical axis.

Any continuous-time signal can be expressed as a combination of even and odd components.

Here, the first component on the right side is an even function, while the second component is odd.

A complex signal can be decomposed into even and odd components using conjugate symmetries.

The product of an even function and an odd function is an odd function. Multiplying two functions of the same type, either both even or odd, will result in an even function.

Lastly, adding or subtracting two even functions will produce an even function, and similarly, adding or subtracting two odd functions will yield an odd function.