This time interval is called the sample interval, si, which is the fundamental period time divided by the number of samples \(N\). For simplicity we will make the time interval between samples equal. The sampling rate, sr, is the number of samples taken over a time period (aka acquisition frequency).The fundamental period, T, is the period of all the samples taken, the time between the first sample and the last.A non-periodic wave does not have a frequency or wavelength. A periodic wave has a frequency \(f\) and a wavelength \(\lambda\) (a wavelength is the distance in the medium between the beginning and end of a cycle, \(\lambda = v/f_0\), where \(v\) is the wave velocity) that are defined by the repeating pattern. Plot(xs,wave.4,type="l",ylim=c(-1.25,1.25)) title("overflowed, non-linear complex wave") abline(h=0,lty=3)Īlso, the Fourier Series only holds if the waves are periodic, ie, they have a repeating pattern (non periodic waves are dealt by the Fourier Transform, see below). If there is, eg, some overflow effect (a threshold where the output remains the same no matter how much input is given), a non-linear effect enters the picture, breaking the sinusoidal wave and the superposition principle. The Fourier Series only holds while the system is linear. Joseph Fourier showed that any periodic wave can be represented by a sum of simple sine waves.
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