FFT of wave packet, strange phase behaviour

Hi,

I'm computing the fft of a wave packet (centred at t= 0, odd number of entries!) to determine its frequency and phase. For this example I created a packet with a frequency of 10Hz and a phase of 1*pi. Waveform plot:

When plotting the fft results I can easily spot the frequency but two things bewilder me:

1. The phase results of the fft jumps continuously between 2*pi and -2*pi.
2. The amplitude also jumps between 0 and positive values. I would expect a lorentz peak centred at my frequency and continuously going down with its width being a measurement for the decay time of the waveform.

Anyone have an explanation for these two things? Is there an error in my code?

 Y3 = fftshift(fft(ifftshift(waveform)));
 subplot(121);
 plot(fVals, abs(Y3));
 subplot(122);
 plot(fVals, angle(Y3));

Thanks in advance!

Fourier Transform Left side is the absolute value of the fourier transform. Right side is the angle.