Table of Contents
- 1 Which function Cannot be expressed as Fourier series?
- 2 Are sin and cos functions periodic?
- 3 Which of the following function Cannot be expanded as a Fourier series?
- 4 Is cosine periodic?
- 5 What is the condition that satisfy When sum of two periodic functions to produce periodic function?
- 6 Why are sine and cosine waves the easiest of the periodic functions?
- 7 Why do we use periodic functions to represent waves?
- 8 Is the shape of a wave a sine or cosine function?
Which function Cannot be expressed as Fourier series?
In fact, almost all periodic functions cannot be expressed as Fourier series.
Are sin and cos functions periodic?
Sine and cosine are periodic functions, which means that sine and cosine graphs repeat themselves in patterns. You can graph sine and cosine functions by understanding their period and amplitude. Sine and cosine graphs are related to the graph of the tangent function, though the graphs look very different.
Is sum of 2 periodic functions always periodic?
Unlike the continuous case, given two discrete periodic signals, their sum is always periodic. We give a characterization for the period of the sum; as shown, the least common multiple of the periods of the signals being added is not necessarily the period of the sum.
Which of the following function Cannot be expanded as a Fourier series?
→ The frequency of first term frequency of 2nd term is ω2 = 1. So, x(t) is a periodic or not periodic. Since function in (b) is non periodic. So does not satisfy Dirichlet conditionand cannot be expanded in Fourier series.
Is cosine periodic?
The cosine function is a trigonometric function that’s called periodic. In mathematics, a periodic function is a function that repeats itself over and over again forever in both directions. This interval from x = 0 to x = 2π of the graph of f(x) = cos(x) is called the period of the function.
Why cosine function and secant functions are periodic?
Since the value of all trignometric functions repeat with an initerval of 0 to 2πrad, hence, they all are periodic. The sine and cosine functions take values between -1 to +1 only. But the functions like tangent, colangent, secant and cosecant can take values between o to ∞ both positive and negative.
What is the condition that satisfy When sum of two periodic functions to produce periodic function?
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.
Why are sine and cosine waves the easiest of the periodic functions?
In order to understand in a simple way, the way the waves, that you are considering, behave in a similar way to the functions of a sine wave. They have properties similar to them and so the sine and cosine waves are the easiest of the periodic functions to represent them.
Why is the sum of Sine and cosine is isomorphic to periodic functions?
Since this is the case and dealing with sine and cosine is mathematically simpler than the general case of periodic functions, why worry about the latter, when you can always express any function as a sum of sines and cosines, and a solution in this form is completely isomorphic with the general case. Share Cite Improve this answer
Why do we use periodic functions to represent waves?
But, this periodic function makes representation a lot more easier. It is much easier to understand the properties of waves when we use sine and cosine graphs to describe them. They closely represent these waves in their propagation.
Is the shape of a wave a sine or cosine function?
Waves really look similar to the shapes of a sine or cosine function, but does this guarantee that expressions that show wave-like movement are sine or cosine functions or is this just an approximation? wavesfourier-transform Share Cite Improve this question