Sure, let's go through each of these signals one by one:

(a) x[n]= cos(0.3 πn) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3π, so the period is 2π/(0.3π) = 20/3, which is not an integer. However, in discrete-time signals, the period should be an integer. Therefore, we can say that the signal is not periodic in the discrete sense.

(b) x [n]= cos(0.3 πn+0.5 π) u[n]
This signal is also not periodic in the discrete sense for the same reason as above. The addition of a phase shift does not change the fundamental frequency of the signal.

(c) x[n]= cos(0.3 πn)+ cos(0.5 πn)
This signal is the sum of two cosine signals. Each of the cosine signals is not periodic in the discrete sense (as explained above), and therefore their sum is also not periodic.

(d) x [n]= cos(0.3 n) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3, so the period is 2π/0.3, which is approximately 20.94. This is not an integer, so we can say that the signal is not periodic in the discrete sense.

Question

Sure, let's go through each of these signals one by one:

(a) x[n]= cos(0.3 πn) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3π, so the period is 2π/(0.3π) = 20/3, which is not an integer. However, in discrete-time signals, the period should be an integer. Therefore, we can say that the signal is not periodic in the discrete sense.

(b) x [n]= cos(0.3 πn+0.5 π) u[n]
This signal is also not periodic in the discrete sense for the same reason as above. The addition of a phase shift does not change the fundamental frequency of the signal.

(c) x[n]= cos(0.3 πn)+ cos(0.5 πn)
This signal is the sum of two cosine signals. Each of the cosine signals is not periodic in the discrete sense (as explained above), and therefore their sum is also not periodic.

(d) x [n]= cos(0.3 n) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3, so the period is 2π/0.3, which is approximately 20.94. This is not an integer, so we can say that the signal is not periodic in the discrete sense.

Knowee AI · Accepted Answer

Sure, let's go through each of these signals one by one:

(a) x[n]= cos(0.3 πn) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3π, so the period is 2π/(0.3π) = 20/3, which is not an integer. However, in discrete-time signals, the period should be an integer. Therefore, we can say that the signal is not periodic in the discrete sense.

(b) x [n]= cos(0.3 πn+0.5 π) u[n]
This signal is also not periodic in the discrete sense for the same reason as above. The addition of a phase shift does not change the fundamental frequency of the signal.

(c) x[n]= cos(0.3 πn)+ cos(0.5 πn)
This signal is the sum of two cosine signals. Each of the cosine signals is not periodic in the discrete sense (as explained above), and therefore their sum is also not periodic.

(d) x [n]= cos(0.3 n) u[n]
This signal is periodic. The period of a discrete-time cosine signal cos(ωn) is given by 2π/ω. Here, ω = 0.3, so the period is 2π/0.3, which is approximately 20.94. This is not an integer, so we can say that the signal is not periodic in the discrete sense.

Q.(1) Determine whether the following DT signals are periodic or not. If periodic, find the period.(a) x[n]= cos(0.3 πn) u[n] (b) x [n]= cos(0.3 πn+0.5 π) u[n](c) x[n]= cos(0.3 πn)+ cos(0.5 πn) (d) x [n]= cos(0.3 n) u[n

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