If you could leave some thoughts on the following, it would be really helpful.

1) In wikipedia (https://en.wikipedia.org/wiki/Cyclostationary_process) one can find the definition of a wide sense cyclostationary process as the stohastic process in which $$E[X(t)] = E[X(t+T_0)] ,\forall t$$ $$R_x(t,\tau) = R_x(t+T_0,\tau) ,\forall t,\tau$$

Then, because $R_x$ is periodic it can be expanded in Fourier Series as $$R_x(t,\tau)= \sum_{n = -\infty}^{\infty} R_x^{n/T_0}(\tau)\cdot e^{i2\pi \cdot n/T_0 \cdot t}$$ In the last sentence (in wikipedia) it says: "Wide-sense stationary processes are a special case of cyclostationary processes with only $ R_{x}^{0}(\tau )\neq 0$."

But if that is true, I can conclude that $$R_x(t,\tau)= R_x^{0}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2} R_x(t,\tau) dt$$

I suspect an error here. If anyone could say anything useful what maybe the writer wanted to say about it, I would be grateful. Thanks in advance.

2) In university the professor told us that a cyclostationary process $\{X(t)\}$ becomes a wss process when we add a rv $\theta$ with uniform distribution like this $\{X(t+\theta)\}$ And then we can calculate the spectral density: $$S_{xx}(f) = \int_{-\infty}^{\infty}\overline{R}_{x}(\tau) \cdot e^{-i2\pi f\tau}d\tau$$ where $$\overline{R}_{x}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2}R_x(t,\tau)dt$$ (which is equal to $R_x^{0}(\tau)$)

I cannot see how the uniformly distributed variable is connected to the above.

If you could leave some thoughts on the following, it would be really helpful.

1)

In Wikipedia one can find the definition of a wide sense cyclostationary process as the stohastic process in which $$E[X(t)] = E[X(t+T_0)] ,\forall t$$ $$R_x(t,\tau) = R_x(t+T_0,\tau) ,\forall t,\tau$$

Then, because $R_x$ is periodic it can be expanded in Fourier Series as $$R_x(t,\tau)= \sum_{n = -\infty}^{\infty} R_x^{n/T_0}(\tau)\cdot e^{i2\pi \cdot n/T_0 \cdot t}$$ In the last sentence (in wikipedia) it says: "Wide-sense stationary processes are a special case of cyclostationary processes with only $ R_{x}^{0}(\tau )\neq 0$."

But if that is true, I can conclude that $$R_x(t,\tau)= R_x^{0}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2} R_x(t,\tau) dt$$

I suspect an error here. If anyone could say anything useful what maybe the writer wanted to say about it, I would be grateful. Thanks in advance.

2)

In university the professor told us that a cyclostationary process $\{X(t)\}$ becomes a wss process when we add a rv $\theta$ with uniform distribution like this $\{X(t+\theta)\}$ And then we can calculate the spectral density: $$S_{xx}(f) = \int_{-\infty}^{\infty}\overline{R}_{x}(\tau) \cdot e^{-i2\pi f\tau}d\tau$$ where $$\overline{R}_{x}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2}R_x(t,\tau)dt$$ (which is equal to $R_x^{0}(\tau)$)

I cannot see how the uniformly distributed variable is connected to the above.

In wikipedia (https://en.wikipedia.org/wiki/Cyclostationary_process) one can find the definition of a wide sense cyclostationary process as the stohastic process in which $$E[X(t)] = E[X(t+T_0)] ,\forall t$$ $$R_x(t,\tau) = R_x(t+T_0,\tau) ,\forall t,\tau$$

Then, because $R_x$ is periodic it can be expanded in Fourier Series as $$R_x(t,\tau)= \sum_{n = -\infty}^{\infty} R_x^{n/T_0}(\tau)\cdot e^{i2\pi \cdot n/T_0 \cdot t}$$ In the last sentence (in wikipedia) it says: "Wide-sense stationary processes are a special case of cyclostationary processes with only $ R_{x}^{0}(\tau )\neq 0$."

But if that is true, I can conclude that $$R_x(t,\tau)= R_x^{0}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2} R_x(t,\tau) dt$$

I suspect an error here. If anyone could say anything useful what maybe the writer wanted to say about it, I would be grateful. Thanks in advance.

EDIT: In university the professor told us that a cyclostationary process $\{X(t)\}$ becomes a wss process when we add a rv $\theta$ with uniform distribution like this $\{X(t+\theta)\}$ And then we can calculate the spectral density: $$S_{xx}(f) = \int_{-\infty}^{\infty}\overline{R}_{x}(\tau) \cdot e^{-i2\pi f\tau}d\tau$$ where $$\overline{R}_{x}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2}R_x(t,\tau)dt$$ (which is equal to $R_x^{0}(\tau)$)

I cannot see how the uniformly distributed variable is connected to the above.

If you could leave some thoughts on the following, it would be really helpful.

1) In wikipedia (https://en.wikipedia.org/wiki/Cyclostationary_process) one can find the definition of a wide sense cyclostationary process as the stohastic process in which $$E[X(t)] = E[X(t+T_0)] ,\forall t$$ $$R_x(t,\tau) = R_x(t+T_0,\tau) ,\forall t,\tau$$

Then, because $R_x$ is periodic it can be expanded in Fourier Series as $$R_x(t,\tau)= \sum_{n = -\infty}^{\infty} R_x^{n/T_0}(\tau)\cdot e^{i2\pi \cdot n/T_0 \cdot t}$$ In the last sentence (in wikipedia) it says: "Wide-sense stationary processes are a special case of cyclostationary processes with only $ R_{x}^{0}(\tau )\neq 0$."

But if that is true, I can conclude that $$R_x(t,\tau)= R_x^{0}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2} R_x(t,\tau) dt$$

I suspect an error here. If anyone could say anything useful what maybe the writer wanted to say about it, I would be grateful. Thanks in advance.

2) In university the professor told us that a cyclostationary process $\{X(t)\}$ becomes a wss process when we add a rv $\theta$ with uniform distribution like this $\{X(t+\theta)\}$ And then we can calculate the spectral density: $$S_{xx}(f) = \int_{-\infty}^{\infty}\overline{R}_{x}(\tau) \cdot e^{-i2\pi f\tau}d\tau$$ where $$\overline{R}_{x}(\tau) = 1/T_0 \int_{-T_0/2}^{T_0/2}R_x(t,\tau)dt$$ (which is equal to $R_x^{0}(\tau)$)

I cannot see how the uniformly distributed variable is connected to the above.