One of the confronting challenges for storage-ringbased light sources to serve time-resolved experiments is online and quantitative measurements of temporal information such as bunch lengths, phases, and currents of stored bunches which are separated by 2 ns with a duration of tens of picoseconds. We demonstrated a compact online diagnostics which enables simultaneous measurements of such temporal information by directly observing the visible part of synchrotron radiation using a fast photodiode and wide bandwidth analogue devices consisting of a bias tee, a pre-amplifier, a digitizer, and cables. A new dedicated signal analysis model capable of compensating for the nonlinear frequency response of the wideband device was developed and compared with a conventional Gaussian deconvolution method that assumes linear frequency responses and perfect Gaussian signal shapes in all calculations. As a result, we show that the new method with the online-diagnostics provides a better estimation of the pulse duration with smaller fit errors and it simultaneously matches the fit curve to the impulse response result of the system measured with a femtosecond laser. The minimum measurable bunch length and bunch current resolution of this system were estimated to be approximately 12 ps and 9 µA, respectively.