Figure 11.11 shows several levels of harmonic reconstruction. The amplitude coefficients, A m, are plotted on a log 10 scale so the smaller values are magnified and are therefore visible. Note that the low-frequency coefficients are large in amplitude, whereas the high-frequency coefficients contain little energy and do not contribute substantially to the reconstruction. Figure 11.10 plots the coefficients for the cosine series representation as a function of the harmonic number. Figures 11.10 and 11.11 illustrate a harmonic reconstruction of an aortic pressure waveform obtained by applying a Fourier series approximation. In Matlab, we can find the Fourier coefficients and plot the partial sums of the Fourier series using the techniques mentioned.In practice, many periodic or quasi-periodic biological signals can be accurately approximated with only a few harmonic components. Conclusionįourier series is used in mathematics to create new functions using sine and cosine waves. Symsum (a (f, x, z, P) * cos (z * pi * x / P) + b (f, x, z, P) * sin (z * pi * x / P), z, 1, n) Īs we can see, we have the plot for our input straight line function and the 4 th partial sum of Fourier series. Our plot will also show the input absolute function.Ī = (f, x, z, P) int (f * cos (z * pi * x / P) / P, x,- P, P) Next, we will plot the partial sum for n = 4. Symsum (a (f, x, Z, P) * cos (z *pi * x / P) + b (f, x, z, P) * sin (z * pi * x / P), z, 1, n) įor this example, we will calculate the 2 nd partial sum of an absolute function.
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