Problem in Windowed FFT output

I have taken a windowed FFT (5 second interval) of a 30 second signal. The 2nd, 3rd, 4th and 5th windows are output as expected. However the first window(shown in blue in the image) has an unusual pattern. See the attached image of the FFT plot (X-axis : Frequency, Y-axis is the Amplitude of the FFT) Sampling Frequency is 500Hz.

Can anyone help me understand why this is happening?

[dpb]

No image attached; we won't be able to do anything with it anyway; attach the actual data as .mat file.

[Aquatris]

My guess is your first window includes transient or irregular measurements in the beginning of the signal. What type of signal is this? Show us the time plot as well.