Fourier Transforms Flashcards
What does a Fourier series do?
Represents a periodic function as a sum of sines and cosines to find frequency/wavelength components
What does a0 represent?
The average of the function
What does a square wave consist of?
Sine terms and the odd harmonics
Definition of odd function
Reflection in y-axis with an inversion f(x)=f(-x)
Definition of even function
Reflection in y-axis f(x)=-f(-x)
FS of an even function
Only contains cos terms (bn’s are zero)
FS of an odd function
Only contains sin terms (an’s are zero)
Way of simplifying with symmetry
Don’t need to split integration, just multiply by 2
What does a Fourier transform do?
Represents a non periodic function
What does the FT of a single pulse look like
A continuum
Type of function produced by a FT
a sinc(x) function - sinx/x
Relationship with top hat and its FT
The width of the FT is inversly proportional to the width of the top hat
FT of even and odd functions
Even - Real Transform Odd - Complex Transform
Definition of convolution
Mathematical function taking two functions and outputting a third
Physical Application of convolution
One function is being measured One function is the response of the measuring system The output is the combination and what we actually receive as the measurement
