E1: Choose the first function. Activate Integral. The cosine coefficient of the 10th order will be calculated for a sawtooth that is symmetrical to the center of the interval. Adjust the amplitude with slider a. Except for a factor of π, the end value of the blue integral line is the coefficient Study the curves and compare them to the formula. What creates the phase jump at π ?
Do the same with the second selection (sine coefficient of sawtooth)
E2: Change the symmetry point with slider b and repeat the experiment. What do you conclude?
E3: Change the order of harmonic step by step (n) and note the coefficients. Draw 2 spectra (coefficients versus order).
E4: Choose the rectangle (used in primitive electronic sounds) and repeat the above experiments. Choose all orders of sine and cosine.
E5: Shift the pulse with slider b and repeat the experiments. Explain the difference to the symmetrical situation.
E6: Draw spectra for the rectangle pulse. Investigate the relation of the harmonic order and the signs of the coefficients.Try to understand this by studying the curves.
E7: Change the width of the rectangle and study the influence on the spectrum.
E8: Choose the Gaussian and perform analogous experiments
E9: Draw general conclusions about which characteristics of function lead to certain types of spectra.
E10: Consider how in Fourier analysis functions are assumed to continue beyond the limits of the fundamental period.