Systems and methods for derivative level-crossing sampling
The derivative of an input signal is level-crossing-sampled and the resulting samples are transmitted. At the receiver, the resulting samples are fed to a zero-order hold followed by an integrator, which results in piecewise-linear reconstruction. The systems and methods are further refined to reduce the number of samples generated per unit of time, compared to methods based on zero-order-hold reconstruction, for a given signal-to-error ratio, without significant hardware overhead.
1. A system for reconstructing an input signal comprising:
a differentiator configured to receive the input signal and generate a first signal representing the first derivative of the input signal;
a level-crossing sampling block configured to receive the first signal and generate level-crossed samples;
a zero-order holding block configured to receive the level-crossed samples and generate a quantized signal; and
an integrator configured to receive the quantized signal and generate a second signal representing a reconstructed signal of the input signal;
wherein the quantized signal is generated using non-uniform quantization.
2. The system of claim 1 , wherein the differentiator is further configured to scale the received input signal.
3. The system of claim 1 , wherein the integrator is further configured to scale the received quantized signal.
4. The system of claim 1 , wherein the level-crossing sampling block is at a transmitter and the zero-order holding block is at a receiver.
5. A method for reconstructing an input signal comprising:
receiving by a differentiator the input signal and generating a first signal representing the first derivative of the input signal;
receiving by a level-crossing sampling block the first signal and generating level-crossed samples of the first signal;
receiving by a zero-order holding block the level-crossed samples and generating a quantized signal; and
receiving by an integrator the quantized signal and generating a second signal representing a reconstructed signal of the input signal;
wherein the quantized signal is generated using non-uniform quantization.
6. The method of claim 5 , wherein the differentiator is further configured to scale the received input signal.
7. The method of claim 5 , wherein the integrator is further configured to scale the received quantized signal.
8. The method of claim 5 , wherein the level-crossing sampling block is at a transmitter and the zero-order holding block is at a receiver.
9. A method for reconstructing an input signal comprising:
receiving by a first differentiator the input signal and generating a first signal representing the first derivative of the input signal;
receiving by a second differentiator the first signal and generating a second signal representing the second derivative of the input signal;
receiving by a controller the second signal and generating a quantization step;
receiving by a level-crossing sampling block the first signal and the quantization step and generating level-crossed samples;
receiving by a zero-order holding block the level-crossed samples and the quantization step and generating a quantized signal; and
receiving by an integrator the quantized signal and the quantization step and generating a third signal representing a reconstructed signal of the input signal.
10. The method of claim 9 , further comprising scaling by the first differentiator the received input signal.
11. The method of claim 9 , further comprising scaling by the second differentiator the received first input signal.
12. The method of claim 9 , further comprising scaling the received quantized signal.
13. The method of claim 9 , wherein the quantizer is configured to generate a small quantization step, when a magnitude of the second signal is small.
14. The method of claim 9 , wherein the quantizer is configured to increase the quantization step when an absolute value of the second signal increases.
15. The method of claim 9 , wherein the level-crossing sampling block is at a transmitter and the zero-order holding block is at a receiver.
16. The method of claim 9 , wherein the quantizer is configured to generate the quantized signal using non-uniform quantization.