The LCD impulse response is a composition of scanning system and response of the luminance element. The type of the scanning system determines the period of the driving signal. For example, since the electron gun in CRT performs a raster scan at 60Hz, so each phosphor is illuminated once every 1/60 second. The illumination period is very short because as soon as the electron gun leaves the phosphor, the phosphor does not illuminate. Therefore the driving signal can be modeled as a short pulse. But for LCD (hold type in particular), the liquid crystal stays ON for the entire 1/60 seconds. Therefore, the driving signal for LCD has to be a long pulse with period 1/60 second. Recently, there are scanning types LCD so in this case the sample-hold time will be shorter than the hold-type ones.
The response of the luminance element determines how fast can the device responds. By observing typical impulse response from experiments, an exponential decay characteristic is used to model the transient behavior of the liquid crystal when a signal falls from 1 to 0. In this model, the tunable parameter is the decay time constant $\alpha$. For better LCD panels, the liquid crystal responds faster and hence the decay time constant is larger. In the idea case where the device responds immediately (e.g, CRT), then the time constant is infinite.
To analyse the blur caused by the two systems, we consider an image with a white strip moving at a speed of v_x. The displayed signal is essentially the weighted average over a few previous frames, with the weights defined by the impulse response of the LCD. In the figures below, the input signals for the two different methods are shown. Note that in the equation below, $x$ is chosen to be a pixel at the far right.
The input and output relationship of the LCD response is essentially the convolution. In the real computation, the convolution is both time and spatial domain. However we only discuss the time domain convolution and assume $x$ to be a pixel at the far right. Now with the input signal shown above, and the transfer function provided, we can compute the output signal as follows.
For Method 1, the out signal is the convolution of input and the transfer function. Therefore, we have the following equations. The figures on the right illustrates the effect of different $alpha$ and different $v_x$. As see, the rise of the signal is stable, and the peak is unity.
Similarly, Method 2 is also calculated. However, as shown in the figures on the right, the intensity is oscillating at different time instants. Also, the peak never reaches unity.