Kefei,
To convert I/Q data to spectrum, you will need to perform overlapping windowed FFTs. Typically what this looks like, if you are doing a 1024-point complex FFT, is every N samples (for your application this would be every 1 ms), you will take the last 1024 I/Q samples, window them (multiply by a window function, like a flat top or hamming window), and then FFT them to generate a spectrum.