a continuous time signals x(t) which is neither odd (or) even can be expressed as a sum of even and odd signals let x(t)=xe(t)+xo(t) =xe(t)= even part of x(t) =xo(t)=odd part of x(t)
Symmetrical signals, or odd functions, exhibit symmetry about the origin, meaning that their waveform is unchanged when reflected across both axes. As a result, the Fourier series representation of such signals contains only odd harmonics, since even harmonics would require symmetry about the vertical axis, which is not present. This absence of even harmonics is a consequence of the mathematical properties of odd functions, where all the even coefficients in their Fourier expansion become zero. Thus, symmetrical signals fundamentally do not include even harmonics.
Yes it would Even + even = even Even + odd = odd Odd + odd = even
Best example is that an "odd" (or "even") function's Maclaurin series only has terms with odd (or even) powers. cos(x) and sin(x) are examples of odd and even functions with easy to calculate Maclaurin series.
because that's the theory of maths even x even = even even x odd = odd even + even = even even + odd = odd
all the signals can not be categorized as even and odd,signals like voice we can not categorize it as even or odd either we can say it is a complex signal.
a continuous time signals x(t) which is neither odd (or) even can be expressed as a sum of even and odd signals let x(t)=xe(t)+xo(t) =xe(t)= even part of x(t) =xo(t)=odd part of x(t)
Symmetrical signals, or odd functions, exhibit symmetry about the origin, meaning that their waveform is unchanged when reflected across both axes. As a result, the Fourier series representation of such signals contains only odd harmonics, since even harmonics would require symmetry about the vertical axis, which is not present. This absence of even harmonics is a consequence of the mathematical properties of odd functions, where all the even coefficients in their Fourier expansion become zero. Thus, symmetrical signals fundamentally do not include even harmonics.
Odd. Even + Even = Even Odd + Odd = Even Odd + Even = Even + Odd = Odd
even times even = even odd times even = even odd times odd = odd
odd * odd = odd answer even * even = even answer odd * even = even answer
Yes. Even + Even = Even, Odd + Odd = Even and Even + Odd or Odd + Even = Odd
No. Sum of odd + odd = even Sum of odd + even = odd Sum of even + even = even
Always. even + even = even odd + odd = even even + odd = odd odd + even = odd To summarise, if you add like numbers you get even, otherwise you get odd.
even times even = even odd times even = even odd times odd = odd
it is even
even times even = even odd times odd = odd even times odd = even