What is the relationship between continuous-time signals and discrete-time signals?

What is the relationship between continuous-time signals and discrete-time signals?

A signal is considered to be a continuous time signal if it is defined over a continuum of the independent variable. A signal is considered to be discrete time if the independent variable only has discrete values.

What is the relation between continuous-time and discrete-time systems?

A system is continuous-time (discrete-time) when its I/O signals are continuous-time (discrete-time). Examples: Despite having different physical origins, these systems have similar mathematical representations.

What is the major difference between continuous-time Fourier transform and discrete-time Fourier transform?

The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions x(t) with a continuous variable t∈R, whereas the DTFT is for discrete-time signals, i.e., for sequences x[n] with n∈Z.

What is the difference between continuous and discrete signal?

A signal, of which a sinusoid is only one example, is a sequence of numbers. A continuous-time signal is an infinite and uncountable set of numbers, as are the possible values each number can have.

Is a device that converts a continuous time signal?

Explanation. An ADC converts a continuous-time and continuous-amplitude analog signal to a discrete-time and discrete-amplitude digital signal. The conversion involves quantization of the input, so it necessarily introduces a small amount of error or noise.

Is time in minutes continuous or discrete?

Explanation: Time is a continuous variable, it can take any positive value in an interval. Even when we measure it in minutes, it can be measured with infinite precision, for example: 0.125 minutes or 0.13333 minutes.

Is time continuous or discrete?

Time is a continuous variable. You could turn age into a discrete variable and then you could count it. For example: A person’s age in years.

Is discrete Fourier transform continuous?

A Discrete Fourier Transform is simply the Fourier Transform when it is applied to discrete rather than a continuous signal. An Fast Fourier Transform is a faster version of the DFT that can be applied when the number of samples in the signal is a power of two.

What is a continuous Fourier transform?

The DFT is the discrete-time equivalent of the (continuous-time) Fourier transforms. As with the discrete Fourier series, the DFT produces a set of coefficients, which are sampled values of the frequency spectrum at regular intervals. The number of samples obtained depends on the number of samples in the time sequence.

When are two continuous maps from X to y homotopic?

Two continuous maps from a topological space X to Y are homotopic if one can be continuously deformed into the other. A more precise definition is the following. Two continuous maps f0 and f1 from X to Y are homotopic if there is a continuous map (called a homotopy) such that for t = 0 or 1, the restriction of h to X × { t } is ft.

When is a continuous map called a strong deformation retraction?

A continuous map r : X → A is called a strong deformation retraction if it is equal to the map x ↦ h(x, 1), where h : X × [0, 1] → X is a continuous map such that h ( x, 0) = x and h ( x, 1) ∈ A for every x ∈ X, and h ( a, t) = a for every a ∈ A and t ∈ [0, 1].

What is the definition of a continuous time signal?

A continuous-time (CT) signal is a function, s (t), that is defined for all time t contained in some interval on the real line. For historical reasons, CT signals are often called analog signals.

How is a continuous map of a topological space connected?

A continuous map of a topological space into another carries connected sets into connected sets. A product of connected spaces is connected. If A is a connected subset of a topological space and B is any set such that A ⊂ B ⊂ ˉA, then B is connected. Any interval of R, including R itself, is connected.