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#### Fourier Series Example

This WebWorksheet explores the Fourier Series expansion of a squarewave.

Each sinewave displayed in W1 is summed to produce the waveform in W2. The sinewaves are of the form: Where n is odd and f0 is the fundamental frequency of the waveform. The slider controls the number of sinusoids to sum. As more sinewaves are added, the more the waveform in W2 looks like a squarewave.

#### Frequency Spectrum

W3 displays the frequency spectrum of the waveform in W2. Each bar in the plot has the same magnitude and is located at the same frequency as the associated sinusoidal component in W1. The bar amplitudes scale as 1/n and the bars are located at frequency n where n is odd (1, 3, 5, 7, ...).

W3 represents a visual summary of W1, The frequency spectrum also indicates the waveform in W2 can be reconstructed by a sum of sinewaves where the amplitudes and frequencies of the sinewaves are given by the heights and locations of the bars in W3.

#### Gibbs Phenomenon

Notice the discontinuities at the edges of the squarewave exhibit "ringing" or overshoot. This behavior is known as Gibbs Phenomenon and results because the Fourier Series expansion requires an infinite number of sinusoidal terms but only a finite number of terms are provided.