ELE541 Homework Solution Prob 6.1

T_s = 1 sec
UTP = N*T_s
F_f = 1/UTP

A phi
(rad) N M f UTP
(sec) F_f
(Hz)

a 2 0 32 1 1/32 32 1/32

b 1 pi/2 64 13 13/64 64 1/64

c 2 pi/8 64 5 5/64 64 1/64

d 1 0 64 33 33/64 64 1/64

e 1 0 128 65 65/128 128 1/128
f 0.5 pi/8 32 2.5 2.5/32 32 1/32

In case d the signal frequency is 33/64 = 0.5156 Hz The sampling frequency of 1 Hz is not twice the signal frequency. Therefore aliasing will occur.

In case e the signal frequency is 65/128 = 0.509 Hz The sampling frequency of 1 Hz is not twice the signal frequency. Therefore aliasing will occur.

	A	phi (rad)	N	M	f	UTP (sec)	F_f (Hz)
a	2	0	32	1	1/32	32	1/32
b	1	pi/2	64	13	13/64	64	1/64
c	2	pi/8	64	5	5/64	64	1/64
d	1	0	64	33	33/64	64	1/64
e	1	0	128	65	65/128	128	1/128
f	0.5	pi/8	32	2.5	2.5/32	32	1/32