Fast Fourier transform- an Update

In continuation of the earlier effort, I made 2 more experiments and got results, however hacky the methods may appear. The full text of the same is as under- :

I did two more experiments and seem to be tantalizingly close to the intended results, but it the solution has the feel of a hack to me.

Experiment 5

So at this point, I have 41 time domain samples representing fundamental + 30% 3rd harmonics, 20% 5th harmonics, 15% 7th harmonics, 10 % 9th harmonic, and 20% 11th harmonics.

0, 0.853079823, 0.857877516, 0.603896038, 0.762429734, 0.896260999, 0.695656841,0.676188057, 0.928419527, 0.897723205, 0.664562475, 0.765676034, 0.968738879,0.802820512, 0.632264626, 0.814329015, 0.875637458, 0.639141079, 0.696479632,0.954031849, 0.50925641, -0.50925641, -0.954031849, -0.696479632, -0.639141079,-0.875637458, -0.814329015, -0.632264626, -0.802820512, -0.968738879, -0.765676034,-0.664562475, -0.897723205, -0.928419527, -0.676188057, -0.695656841, -0.896260999,-0.762429734, -0.603896038, -0.857877516, -0.853079823.

I did a linear interpolation and derived 64 samples from the same. They looked like the following:

The frequency domain representation compared to the desired ideal output (First experiment) is as under:

I have stripped off the second half of the sample space as the components fold after the Nyquist limit. There is a little attenuation at the frequencies of interest, but a noise floor is added across the spectrum.Explanations?

Experiment 6

Same as Experiment 5, but 32 interpolated samples.

Frequency domain comparison:

The ratios are correct but magnitudes are halved ! Why?

So I may infer, and I may be wrong(I hope I am), that if the number of samples in a complete waveform period are not a power of 2, the FFT of the same does not reveal anything without some kind of an operation, that eludes me at the moment.

Since I have very little control over the sampling frequency, What are the options open to me so as to get back the values that I injected in the time domain?

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