What are the first terms in the Fourier series of the repeating function shown?

What are the first terms in the Fourier series of the repeating function shown?

The first term in a Fourier series is the average value (DC value) of the function being approximated.

How do you find the average value of a Fourier series?

The sum of the Fourier series is equal to f(x) at all numbers x where f is continuous. At the numbers x where f is discontinuous, the sum of the Fourier series is the average value. i.e. The average value is 1/2.

What is an orthogonal set of functions?

As with a basis of vectors in a finite-dimensional space, orthogonal functions can form an infinite basis for a function space. Conceptually, the above integral is the equivalent of a vector dot-product; two vectors are mutually independent (orthogonal) if their dot-product is zero.

What is meant by orthogonal function?

: two mathematical functions such that with suitable limits the definite integral of their product is zero.

What is odd function and even function in Fourier series?

4.6 Fourier series for even and odd functions A function is called even if f(−x)=f(x), e.g. cos(x). A function is called odd if f(−x)=−f(x), e.g. sin(x). These have somewhat different properties than the even and odd numbers: The sum of two even functions is even, and of two odd ones odd.

What is the function of an odd function in Fourier analysis?

A function y=f(t) is said to be odd if f(−t)=−f(t) for all values of t . The graph of an odd function is always symmetrical about the origin. Hence, the Fourier series of an odd periodic function contains only sine terms.

What is periodic function in Fourier series?

In mathematics, a Fourier series (/ˈfʊrieɪ, -iər/) is a periodic function composed of harmonically related sinusoids combined by a weighted summation. The process of deriving weights that describe a given function is a form of Fourier analysis.

What is the Fourier series of a function?

A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine and cosine functions. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms.

Does f(x) = x for x ≥ 2 describe a function?

By convention x unambiguously denotes the non-negative square root of x, so ‘ f ( x) = x for x ≥ 2 ’ does describe a function. However, unless you’ve misunderstood her, your teacher is using the term mapping incorrectly.

What is the domain of the sqrt function?

The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. For negative and complex numbers z = u + i*w, the complex square root sqrt(z) returns. sqrt(r)*(cos(phi/2) + 1i*sin(phi/2))

What does the sqrt function return?

The sqrtfunctions return the square-root of x. By default, if xis negative, sqrtreturns an indefinite NaN. Input SEH Exception

What does sqrt(x) do in Python?

B = sqrt (X) returns the square root of each element of the array X. For the elements of X that are negative or complex, sqrt (X) produces complex results. The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally.