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:

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

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

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:

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

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

What qualities of h[n] are necessary for:

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

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

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

where:

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

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

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:

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

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