Discrete-time Derivative

Dear friends!

I am simulating a system with an ADC which acquires signals from two sensors at some N Hz rate, converting a continuous signal into descrete. I then intend to use an LQR controller for the full state of the system, which consists of four states: the two I can acquire from the sensors and other two I can obtain by means of determination of their derivatives: X=[x; theta; x dot; theta dot]. So I have put in the Discrete-time Derivative block in my Simulink program, but when I compare signal theta dot from the continuous system and the theta dot I get from this derivative block, there seem to occur extremely high peaks where the derivative tends to its local extremum. Please, check the figure I have attached. You can barely see it, but there is also a yellow line showing the actual continuous-time derivative, its maximum amplitude is about 14 and its a slowly damping out oscillation signal. The magnitude of peaks seem to depend on the sampling rate proportionally: at 100 Hz the peaks are at about 600, at 200Hz - at about 1200 and at 50Hz - at about 300. I have no idea where to go with this.

If you have any suggestions or thoughts, please, do share with me!

Best Regards, Alex