#StackBounty: #r #fft Reconstruct Time Series from FFT frequency and strength data using R

Bounty: 100

After applying a Fourier Transform to an EEG measurement, I want to compare the approximation by FFT with the original signal in the form of a plot. I have to convert the data (frequency and strength) from the FFT back to a time series.
To transform the original time series I use the eegfft method of the eegkit package. I get a list of frequencies and amplitudes to approximate the original signal.

Here the two results of the FFT are shown as shortened examples:

# Frequency in Hz
freq <- c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)  

# Strength in uV
ampl <- c(4.1135352, 5.1272713, 3.2069741, 1.5336438, 2.4301334, 1.0974758, 1.8238327, 0.9637886, 1.1401306, 0.2224472)

Is there a package or method that I can use to reconstruct a time series from the frequency and amplitude data that has been approximated by FFT?


EDIT:

For the reconstruction of the original signal, do I also need the phase information that the eegfft method returns in the result?

# Phase shift in range -pi to pi
phase <- c(0.0000000, 1.1469542, -2.1930702, 2.7361738,1.1597980, 2.6118647, -0.6609641, -2.1508755,1.6584852, -1.2906986)


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