Method and apparatus for reducing the contribution of noise to digitally sampled signals
View Patent ↗A method and apparatus for reducing the contribution of noise to digitally sampled signals includes a statistical processor and a slope limiter. The statistical processor determines an average value (mean and/or standard deviation) of the filtered signal which is used to determine a slope limit corresponding to an expected maximum first derivative value of a target signal frequency. This slope limit is applied to constrain the output of an analog to digital converter, to prevent the output of the analog to digital converter from exceeding this maximum rate of rise or fall. By constraining the output of the analog to digital converter, it is possible to digitally sample analog signals without first utilizing an anti-aliasing filter, since the post processing of the digitally sampled signals limits the contribution of the higher frequency components of the signal to thereby enable a fully digital sampling and filtering circuit to be provided for receiving signals.
1. A method of reducing the contribution of noise to filtering digitally sampled signals, the method comprising the steps of:
receiving an analog signal by a receiver;
sampling the analog signal by an analog to digital converter to create a digital representation of the signal without first passing the analog signal through an anti-aliasing filter; and
generating a constrained output signal of the analog to digital converter by applying a slope limit function to the digital representation of the signal to constrain within a limit a rate of rise or rate of fall of an output of the analog to digital converter.
2. The method of claim 1 , wherein the limit corresponds with a maximum first derivative value of a maximum frequency of an output signal from the receiver.
3. The method of claim 2 , wherein the maximum frequency of the output signal from the receiver is at most ½ a sampling frequency at which the analog signal is sampled by the analog to digital converter.
4. The method of claim 3 , wherein the limit further corresponds with an expected amplitude of the analog signal.
5. The method of claim 1 , further comprising the step of applying the constrained output signal to a digital computer for processing by the digital computer.
6. The method of claim 1 , wherein the slope limit function causes the constrained output signal to be equal to a previous constrained output signal plus the limit if the output from the analog to digital converter is more than the limit value higher than a previous output of the analog to digital converter.
7. The method of claim 1 , wherein the slope limit function causes the constrained output signal to be equal to a previous constrained output signal minus the limit if the output from the analog to digital converter is more than the limit value lower than a previous output of the analog to digital converter.
8. The method of claim 1 , wherein the slope limit function compares the output of the analog to digital converter with a moving average calculated using a set of previous constrained output signal values.
9. The method of claim 8 , wherein the moving average is calculated using the set of previous constrained output signal values and, upon application of the slope limit function, the constrained output signal value replaces one of the previous constrained output signal values in the set.
10. The method of claim 1 , wherein the slope limit function compares the output of the analog to digital converter with a standard deviation value calculated using a set of previous constrained output signal values.
11. A receiver, comprising:
an analog to digital converter to receive an analog signal and sample the analog signal according to a sampling function to create a digital representation of the signal, the analog signal containing a noise component having frequency components above the Nyquist Criteria for the sampling function; and
a signal restrictor to receive the digital representation of the signal at each sampling interval of the sampling function and to apply a limit to the digital representation of the signal with respect to a previous iteration of the digital representation of the signal to limit a rate of change of an output of the analog to digital converter between sampling intervals.
12. The receiver of claim 11 , wherein the signal restrictor applies a limit determined to correspond with a maximum first derivative value of a target frequency.
13. The receiver of claim 11 , wherein the signal restrictor applies the limit to the digital representation of the signal with respect to an immediately previous iteration of the digital representation of the signal.
14. The receiver of claim 11 , wherein the signal restrictor applies a slope limit function to cause the output of the analog to digital converter to be equal to a previously constrained value of the digital representation of the signal plus the limit, if the digital representation of the signal is more than the limit value higher than a previous value of the digital representation of the signal.
15. The receiver of claim 11 , wherein the signal restrictor applies a slope limit function to cause the output of the analog to digital converter to be equal to a previously constrained value of the digital representation of the signal minus the limit, if the digital representation of the signal is more than the limit value lower than a previous value of the digital representation of the signal.
16. The receiver of claim 11 , wherein the signal restrictor applies the limit to the digital representation of the signal with respect to a moving average calculated using a set of previous iterations of the digital representation of the signal.
17. The receiver of claim 11 , wherein the signal restrictor applies the limit to the digital representation of the signal with respect to a moving standard deviation calculated using a set of previous iterations of the digital representation of the signal.
18. The method of claim 1 , wherein the slope limit function causes the constrained output signal to be the same as the output of the analog to digital converter if the output from the analog to digital converter is less than the limit value higher than a previous output of the analog to digital converter or is less than the limit value lower than the previous output of the analog to digital converter.
19. The receiver of claim 11 , wherein the signal restrictor applies a slope limit function to cause the digital representation of the signal to be unchanged after being output by the analog to digital converter if the digital representation of the signal is less than the limit value higher or less than the limit value lower than a previous value of the digital representation of the signal.