Discrete Sinusoidal to State Space

1. What is discrete sinusoidal signal?
2. What is the condition for dt sinusoidal sequence to be periodic?
3. What are the key differences between continuous-time and discrete-time sinusoids?

What is discrete sinusoidal signal?

A sinusoidal signal which is defined only at discrete instants of time is called discrete-time sinusoidal signal. The discrete-time sinusoidal signal is given as follows − 𝑥(𝑛) = 𝐴 sin(𝜔𝑛 + 𝜑) = 𝐴 sin(2𝜋𝑓𝑛 + 𝜑) Where, A is the amplitude of the signal.

What is the condition for dt sinusoidal sequence to be periodic?

Therefore, a discrete-time sinusoid is periodic if its radian frequency Ω is a rational multiple of π. Otherwise, the discrete-time sinusoid is non-periodic.

What are the key differences between continuous-time and discrete-time sinusoids?

ii) One cycle corresponds to the angle of a discrete- time sinusoid changing by 2πm radians where m is integer. b) Frequency of a continuous-time sinusoid is measured in cy- cles/second (Hertz - Hz), or radians/second. c) Frequency of a discrete-time sinusoid is measured in radi- ans/sample or radians.