Is the sum of 2 periodic functions periodic?

The answer is well known in the case when two nonconstant periodic functions are defined and continuous on the whole real line and the operation is addition. In this case the sum is periodic if and only if the periods of summands are commensurable.

Is the sum of periodic functions always periodic?

Sums of periodic functions are not always periodic , whose terms have least periods 2π and 2 respectively.

Can the sum of two non periodic functions be periodic?

Yes, it is possible. For example, , satisfy the property. is clearly periodic, and the sum, which is is also periodic.

What is the sum of two periodic signals?

Sum of two periodic signals is a periodic signal when the ratio of their time periods is. Explanation: sum of two periodic signals is a periodic signal only when the ratio of their time periods is a rational number or it is the ratio of two integers. for e.g., t1/t2 = 5/7 → periodic; t1/t2 = 5 → aperiodic.

What are periodic signals?

A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. Examples of periodic signals include the sinusoidal signals and periodically repeated non-sinusoidal signals, such as the rectangular pulse sequences used in radar.

How do you know if a signal is periodic?

A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. In mathematical terms a signal x(t) is periodic if there is a number T such that for all t Equation 10.10 holds.

What is periodic and non periodic?

10.5. 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. In principle this includes all actual signals since they must start and stop at finite times.

Is periodic or not?

A function f(x) is said to be periodic, if there exists a positive real number T such that f(x+T) = f(x). The smallest value of T is called the period of the function. 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.

Is sin 3n periodic?

Member level 3. if n represents an interval greater than 2*2pi; yes it is periodic.

What is non-periodic signal?

Non-periodic signals (also known as aperiodic signals), unlike periodic signals, do not have just one particular frequency. Instead, they are spread out over a continuous range of frequencies.

Is the sum of two time varying functions periodic?

A continuous-time signal consisting of the sum of two time-varying functions is periodic, if and only if both functions are periodic and the ratio of these two periods is a rational number. In such a case, the least common multiple of the two periods is the period of the sum signal.

How do you find the sum of two periodic signals?

Then k*T1 or l*T2 will be equal to the period (only if l/k is rational) of the resultant signal which is the sum of the two periodic signals. N.B: if any of them is not periodic, then the resultant signal will not be periodic, if any of them is unbounded (and the rest one periodic), then, the resultant will also be unbounded.

What is the difference between periodic and physical signals?

As already emphasized, periodic signals have an infinite energy whereas those which correspond to physical quantities have a finite power. As a consequence, the concept of functions and coefficients of correlation can be extended to such periodic signals, provided power is used instead of energy.

What is the period of the sum of two periods?

A continuous-time signal consisting of the sum of two time-varying functions is periodic, if and only if both functions are periodic and the ratio of these two periods is a rational number. In such a case, the least common multiple of the two periods is the period of the sum signal.