Sinusoidal Steady-State Response of Digital Filters - Digital Signal Processing: Fundamentals and Applications - page 816

Based on Equation (D.24) , we also obtain the magnitude and phase response for Hðe j U Þ as

q

ðb 0 þ b 1 cos U þ / þ b M cos M U Þ

2 2

Hðe j U Þ ¼ þðb 1 sin U þ / þ b M sin M U Þ

q

ð 1 þ a 1 cos U þ / þ a N cos N U Þ

(D.27)

2 2

þða 1 sin U þ / þ a N sin N U Þ

: Hðe j U Þ¼ tan 1 b 1 sin U þ / þ b M sin M U
b 0 þ b 1 cos U þ / þ b M cos M U

tan 1 a 1 sin U þ / þ a N sin N U
1 þ a 1 cos U þ / þ a N cos N U

(D.28)

Comparing Equation (D.25) with (D.27), and Equation (D.26) with (D.28), respectively, we obtain the
symmetric properties as

Hðe j U Þ ¼ Hðe j U Þ

(D.29)

: Hðe j U Þ¼ : Hðe j U Þ

(D.30)