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WAHEGURU….!

Fourier Series and ………….

Ok first of all according to Sir Leonardo “imagination is everything”. We are lucky we have brain to imagine the things. My imagination if Using the fourier or discreate fourier transformation we can create the \$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$Fourier Series->Vibrations->Transformations with power packed with SageMath Civil people can solve all the vibration  problems only with few clicks\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$\$ Well even I have no idea yet what the problems civil Engineers face with Vibrations. 😀 😉 (Imagination+believe) Ok First of I need to understand Fourier Series. Fourier Series: It decomposes Periodic functions or periodic signals into sum of simple oscillating functions. Simple oscillating functions can Sines,cosines or complex exponential. ################################################################################################# IN SIMPLE:Periodic function = Simtion(i=0,n)[Xn] Were n= number of sets and X=osculating function ################################################################################################# But that is not enough of the Fourier series learning: Periodic functions: (Ctrl+c Ctrl+v from Wikipedia :D) In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of 2π radians. Osculating Functions:  Seems little difficult let’s start with Oscillation. (simple) Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Ok that means in my language it is just a graph that how the values changes from -ve to +ve value in some interval of time For example Alternate current. (AC) Ahh, got you. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating human heart, business cycles in economics, predator-prey population cycles in ecology, geothermalgeysers in geology, vibrating strings in musical instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. Ok now feels I am the following kind of situation: