Graph of periodic square wave function.For this function, we have: f(t)=−3f(t)=−3 for −1≤t<1−1≤t<1 and 33 for 1≤t<31≤t<3 f(t)=f(t+4)f(t)=f(t+4) [The period is 4.] NOTE: In this example, the period p=4p=4. We can write this as 2L=42L=4....
book there is an example of making a square wave by "simply" summing up a few cosine waves. The book says these first three waves are the first three Fourier components of a square wave, yet when I sum the three wave functions up, I get something way off; as does my calculator......
In fact, this is as easy as multipling and adding numbers – we take the ‘reference’ sine wave of known frequency and unit amplitude (this just means that it has an amplitude of 1, which is exactly what we get back from the sin() function on our pocket calculator or our computer)...
AFourierseriesmaybeused,forexample,toshowthat asquarewaveisthesumofasinewave,andallofit’s oddharmonics. TheFourierSeries(3) Whiletheindependentvariablemaybesomethingotherthantime,andthe Seriesmaybreakthefunctiondownintermsofanycompletesetof Orthogonalfunctions,thisdiscussionwillassumeafunctionoftime, ...