The frequency response of a causal and stable LTI system

The frequency response of a causal and stable LTI system is—
H(jω) = 1 – jω .
1 + jω

The group delay of the system is—

We know that group delay

τ(ω) =	– d	φ(ω)
	dω

∠H (jω) = φ(jω)

= tan^–1		– ω		– tan^–1		– ω
		1				1

or
φ(jω) = – 2 tan^–1 ω

τ(ω) =	– d	(– 2 tan^–1 ω)
	dω

=	2
	1 + ω²

H(jω) =	1 – jω	.
	1 + jω