2 Signals and Systems: Part I Recommended Problems P2.1 Let x(t) = cos(w.(t + T) + 8,). (a) Determine the frequency in hertz and the period of x(t) for each of the follow- ing three cases: (i) 7/3 (ii) 37/4 1/2 T/4 (iii) 3/4 1/2 1/4
2 Signals and Systems: Part I Recommended Problems P2.1 Let x(t) = cos(w.(t + T) + 8,). (a) Determine the frequency in hertz and the period of x(t) for each of the follow- ing three cases: (i) 7/3 (ii) 37/4 1/2 T/4 (iii) 3/4 1/2 1/4
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![2 Signals and Systems: Part I
Recommended
Problems
Р2.1
Let x(t) = cos(w.(t + T) + 6.).
(a) Determine the frequency in hertz and the period of x(t) for each of the follow-
ing three cases:
Tx
(i)
T/3
(ii)
Зп/4
1/2
T/4
(iii)
3/4
1/2
1/4
(b) With x(t) = cos(w,(t + T,) + 6,) and y(t) = sin(w,(t + T,) + 6,), determine for
which of the following combinations x(t) and y(t) are identically equal for all t.
Ty
(i)
T/3
27
7/3
1
-T/3
(ii)
Зт/4
1/2
7/4
117/4
1
37/8
(iii)
3/4
1/2
1/4
3/4
1
3/8
Р2.2
Let x[n] = cos(2(n + P,) + 62).
(a) Determine the period of x[n] for each of the following three cases:
P
(i)
T/3
27
(ii)
Зп/4
2
7/4
(iii)
3/4
1
1/4
(b) With x[n] = cos(2,(n + P) + 0,) and y[n] = cos(2,(n + P,) + 0,), determine
for which of the following combinations x[n] and y[n] are identically equal for
all n.
P,
(i)
*/3
27
87/3
(ii)
37/4
2
T/4
37/4
1
(iii)
3/4
1
1/4
3/4
1
Р2.3
(a)
A discrete-time signal x[n] is shown in Figure P2.3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c057999-aef7-4ec0-8fd1-c99a887a6901%2Fe30bf180-5b22-4a9d-bb2b-eca1ac502749%2Fx88qii8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2 Signals and Systems: Part I
Recommended
Problems
Р2.1
Let x(t) = cos(w.(t + T) + 6.).
(a) Determine the frequency in hertz and the period of x(t) for each of the follow-
ing three cases:
Tx
(i)
T/3
(ii)
Зп/4
1/2
T/4
(iii)
3/4
1/2
1/4
(b) With x(t) = cos(w,(t + T,) + 6,) and y(t) = sin(w,(t + T,) + 6,), determine for
which of the following combinations x(t) and y(t) are identically equal for all t.
Ty
(i)
T/3
27
7/3
1
-T/3
(ii)
Зт/4
1/2
7/4
117/4
1
37/8
(iii)
3/4
1/2
1/4
3/4
1
3/8
Р2.2
Let x[n] = cos(2(n + P,) + 62).
(a) Determine the period of x[n] for each of the following three cases:
P
(i)
T/3
27
(ii)
Зп/4
2
7/4
(iii)
3/4
1
1/4
(b) With x[n] = cos(2,(n + P) + 0,) and y[n] = cos(2,(n + P,) + 0,), determine
for which of the following combinations x[n] and y[n] are identically equal for
all n.
P,
(i)
*/3
27
87/3
(ii)
37/4
2
T/4
37/4
1
(iii)
3/4
1
1/4
3/4
1
Р2.3
(a)
A discrete-time signal x[n] is shown in Figure P2.3.
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