Given the head start from the recitation or lecture $($also recorded$),$ calculate the first $15$ Fourier Coefficients $(+$ the DC coefficient$)$ for the attached data file and print them rounded to $3$ places and labeled to the console.. This data file is a cssv file and represents a single pulse $($heart beat$)$ for the arterial blood volume signal. The time axis is in seconds and the signal is normalized to $1($arbitrary units$).$ The time values are evenly spaced in time.

Fourier Series Background and Formulas

Recall from prior courses the following equations to formulate a Fourier series. Any periodic function, $f(t)$ of period $T,$ can be represented by an infinite number of sinusoidal functions as equation $(1)$ below where $N=.$ The signal can be approximated by a finite number of sinusoids where $N$ is finite. In general, the faster the signal varies with time, then a larger $N$ is needed to approximate the function with a given fidelity or accuracy.

$f(t)=a_0+{\displaystyle \underset{n=1}{\overset{N}{}}}{a}_{n}cos(nt)+b_{n}sin(nt)$

$=2f=\frac{2}{T}(Eq.2)$

Each of the Fourier Coefficients, $a_n$ and $b_n,$ give the amplitude of the sins and cosines at the radian frequency of $n$ that will reconstruct the original signal. Note that $n$ are harmonics of the base signal's frequency $.$ Also note that $a_0$ is the zero frequency, or D$.$C$.$ component which is also the average value of the signal.

$a_0=\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{}}}f(t)dt$

$a_n=\frac{2}{T}{\displaystyle \underset{0}{\overset{T}{}}}f(t)cos(nt)dt$

$b_n=\frac{2}{T}{\displaystyle \underset{0}{\overset{T}{}}}f(t)sin(nt)dt$

ppg norm.csv darr

Plot the original function and the reconstructed function on the same time axis, with a legend. Properly label the axes.

Submit a screen shot showing the console output and the graph. Submit your python code.

Please exercise good coding practices. For example, proper and descriptive variable names, input variables at top of program, concise and descriptive comments.