Fourier Series Flashcards
what are the basis function for a real fourier series
- sin(t), sin(2t), sin(3t) etc…
- cos(t), cos(2t), cos3(t) etc…
what is the forurier series general formula f(t)
f(t) = d + Σ(n=1 to ∞)[a(n)cos(2πnt/L) + b(n)sin(2πnt/L)]
what is L referring to in the fourier series formula
the period of the signal
what is the formula for the coefficient a(n)
a(n) = (2/L)int[cos(2πnt/L)f(t) dt] from limits L to 0
what is the formula for the coefficient b(n)
b(n) = (2/L)int[sin(2πnt/L)f(t) dt] from limits L to 0
what is the formula for the coefficient d
d = (1/L)*int[f(t) dt] from limits L to 0
what is one thing to note about the integration limits
- the period of the signal’s cycle has to be 2π
- but the integration limits dont have to be from 2π to 0
- it can be from any range
what is f(t) in the formulas for the coefficients
the input signal (usually just given to you)
what is an odd function
- a function that is antisymmetric about the origin
- f(-t) = -f(t) aka sin
what is an even function
- a function that is symmetric about the origin
- f(-t) = f(t) aka cos
what is the easiest way to know whether an f(t) function has an a(n), b(n) or d term
- it only has an a(n) term if the function has an even component
- it only has a b(n) term if the function has an odd component
- it only has a d term if the mean of the function is not 0
how do you deal with discontinuous / dodgy f(t) functions
split the integration into multiple sections and add them up
why dont you just assume that a b(n) and a(n) coefficient cant exist simultaneously
- because of more complex function where its not obvious to say if its even or odd
- it can be both in some cases
how do you quickly figure out the fourier series of common functions
there are some in the databook
