## 1 Introduction
The energy chirp leads to streaking of time into reciprocal space in the diffraction pattern--because different wavelengths diffract to different locations on the detector, diffraction from the earliest energies is physically separated from diffraction caused by the energies arriving later in time. Through Laue indexing, an individual reflection can be assigned to the wavelength that stimulated it, and thus to its specific time within the pulse if there is an energy chirp. With sufficient bandwidth, a deconvolution of multiplicity would additionally be needed, such that the time-to-energy relation could still be extracted. Time-dependent information of the pump-probe experiment is therefore intrinsically present in individual images collected with chirped broadband pulses. The time interval across which structure amplitude differences are recorded is set by the chirp magnitude of the X-ray probe pulse. [PERSON] additionally proposed that if the pump pulse occurs within the probe, each image will also include unpumped reference structure factor amplitudes which will aid the scaling of time-resolved differences [34]. Here, we extend this method to XFEL pulses in order to obtain ultrafast time resolution with the availability of femtosecond energy-chirped hard X-ray pulses and consider the time resolution that could be obtainable. Several numerical simulation codes for SASE FELs have been developed to explore the effects of different beamline components on performance and to aid in the interpretation of experimental results [35; 36; 37; 38]: they provide three-dimensional representations of the pulse by solving the FEL equations [39], which describe both the propagation of the electrons and the evolution of the radiation field. Calculation methods are constantly being improved. A recent version of GENESIS, one of the most widely used codes, is able to simulate the propagation and SASE of the entire electron beam through the undulator [40]. Pulse profiles computed in this way are presented here in order to simulate and assess the time dependence of experimental diffraction. The aim of this work is thus to evaluate the time resolution, \(\Delta\)tres, that would theoretically be achievable in a polychromatic XFEL experiment from considerations of physical parameters for protein crystallography. The X-ray pulse length, spectral bandwidth over time, and chirp magnitude determine the resolution and are obtained through simulations of the XFEL provided by SwissFEL. A ray-tracing simulation demonstrates the chirped diffraction patterns generated by the polychromatic XFEL pulse. It has been shown that a 4% \"extra pink\" beam mode at SwissFEL will probe a large enough volume of reciprocal space to fully integrate multiple reflections [41]. As the polychromatic beam is chirped, it should be possible to identify which spots correspond to different energies and therefore to different points in time. Here, we consider a negative energy chirp, such that diffraction spots that appear at the leading edge of the pulse (tin) are stimulated by the highest energies. When evaluating full reflection integration, it is noted that, while the total spectral bandwidth that generates the polychromatic image is equal to the magnitude of the chirp (e.g., 4%), we analyze the \"instantaneous\" frequency (IF) and \"instantaneous\" bandwidth (BWin) associated with every instance of the pulse that is obtained from Wigner-Ville distribution analysis of the simulated field [42; 43]. The determination of IF in a pulse becomes useful when its spectral characteristics vary over time. The Wigner-Ville distribution (WVD) is a two-dimensional distribution of the signal in the time-frequency domain. Projection of the distribution on one axis results in either the temporal or the spectral structure of the pulse. The IF corresponds to the first moment of the WVD with respect to frequency [44; 45], while BWin is defined as the standard deviation, or spread of frequencies, present at a given time [46].