Your original question said 1 per second. Now you say 1 per day. Which is it?
You say you get a big spike at zero. That is because your signal does not have zero mean. It is shifted upwards - it has a mean of around 1 or 1.5 times ten to the (something) power. That means you have a lot of energy in the DC (zero frequency) component. I don't see the other spikes at the other frequencies - looks basically like random noise to me. Though because your signal is multiplied by a rect (basically a window the entire size of your signal) that means that your Fourier signal will be convolved with a sinc function, though a very narrow one. Sometimes this gives little ringing to the spikes. And of course if your signal is not the same at the left and right on the x axis, you will have a discontinuity which will also introduce higher frequencies. They way to reduce that is to window your signal. Look up Hanning or Hamming Window for more info.
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