What qualities of $h[n]$ are necessary for:

$$
H(e^{j\omega}) = DTFT\{h_{even}[n]\} + j\ DTFT\{h_{odd}[n]\}
$$

**Do all real / causal h[n] have the property that:**

$$
H(e^{j\omega}) = DTFT\{h_{even}[n]\} + j\ DTFT\{h_{odd}[n]\}
$$


where:

$$
h_{even}[n] = \frac{1}{2}(h[n] + h[-n]) 
$$ 

$$
h_{odd}[n] = \frac{1}{2}(h[n] - h[-n]) 
$$