Can a bounded function be periodic?

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Can a bounded function be periodic?

This function is defined for all x∈R and is periodic with period π. This function is not bounded. Of course, if you require f to be continuous, then if the function has (WLOG) period 1, it is bounded on [0,1] because it is continuous. It follows that f is bounded on all of R since it is periodic.

Are sine functions always periodic?

Sin and cos are everywhere continuous and infinitely differentiable. Those are nice properties to have. They come from the unit circle. It seems there’s no other periodic function that is also smooth and continuous.

Is sin 3n periodic?

will be never periodic.

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What is periodic and nonperiodic?

2 Periodic and aperiodic signals. A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. A non-periodic or aperiodic signal is one for which no value of T satisfies Equation 10.11.

Can a sinusoidal function be cosine?

A sine wave, or sinusoid, is the graph of the sine function in trigonometry. (A and B are positive). Sinusoids are considered to be the general form of the sine function. Any cosine function can be written as a sine function.

Are sine functions always continuous?

The function sin(x) is continuous everywhere.

How do you find a function is periodic or not?

  1. A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x).
  2. The smallest value of T is called the period of the function.
  3. Note: If the value of T is independent of x then f(x) is periodic, and if T is dependent, then f(x) is non-periodic.
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Is Sinn periodic?

will be never periodic. it means w0*N=0.

Is sin2n periodic?

sine function is periodic. Hence sin (2t) will also be periodic.

What is the difference between a bounded and unbounded set?

So if S is a bounded set then there are two numbers, m and M so that m ≤ x ≤ M for any x ∈ S. It sometimes convenient to lower m and/or increase M (if need be) and write |x| < C for all x ∈ S. A set which is not bounded is called unbounded. For example the interval (−2,3) is bounded.

Can a periodic function be represented as a linear sum of functions?

However, there’s always the Nyquist theorem, which says that, within a certain sampling error, a periodic function can always be represented as a linear sum of trigonometric (periodic) functions. Linear superposition is not the only way.

How do you know if a set is bounded above?

S is called bounded above if there is a number M so that any x ∈ S is less than, or equal to, M: x ≤ M. The number M is called an upper bound for the set S. Note that if M is an upper bound for S then any bigger number is also an upper bound.

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Does every set of numbers have an upper bound?

Notallsetshave anupperbound. For example, the set ofnatural numbers does not. A number B is called the least upper bound (or supremum) of the set S if: 1) B is an upper bound: any x ∈ S satisfies x ≤ B, and 2) B is the smallest upper bound.