Defeat of aliasing by incremental sampling
A method includes generating a sampling signal having a non-uniform sampling interval and sampling a received signal with an analog-to-digital converter (ADC) using the sampling signal. The method also includes mapping the sampled received signal onto a frequency grid of sinusoids, where each sinusoid has a signal amplitude and a signal phase. The method further includes estimating the signal amplitude and the signal phase for each sinusoid in the frequency grid. In addition, the method includes computing an average background power level and detecting signals with power higher than the average background power level. The non-uniform sampling interval varies predictably.
1. An apparatus comprising:
a signal generator configured to generate a sampling signal with a varying sampling interval having an average time step with a variation size; and
an analog-to-digital converter (ADC) configured to sample a received signal using the sampling signal;
wherein the varying sampling interval is a function of the average time step, the variation size, and a ratio of a current sample number relative to a total number of samples taken;
wherein the varying sampling interval is defined by:
Δ
t
n
=
dt
(
1
-
f
+
2
f
n
n
max
)
wherein n is the current sample number having a sampling interval Δt n , dt is the average time step, f is the variation size, and n max is the total number of samples.
2. The apparatus of claim 1 , wherein the variation size has a value of 0.5.
3. The apparatus of claim 1 , wherein the total number of samples has a value that is an integer multiple of 512.
4. The apparatus of claim 1 , further comprising at least one processing device configured to:
map the sampled received signal onto a frequency grid of sinusoids, each sinusoid having a signal amplitude and a signal phase;
estimate the signal amplitude and the signal phase for each sinusoid in the frequency grid;
compute an average background power level; and
detect signals with power higher than the average background power level.
5. The apparatus of claim 4 , wherein the at least one processing device is further configured to:
remove the signals with the power higher than the average background power level from the sampled received signal; and
repeat the map, estimate, compute, and detect operations.
6. The apparatus of claim 1 , wherein the average time step dt is less than or equal to ten times a Nyquist sampling time.
7. A method comprising:
generating a sampling signal with a non-uniform sampling interval having an average time step with a variation size;
sampling a received signal with an analog-to-digital converter (ADC) using the sampling signal;
mapping the sampled received signal onto a frequency grid of sinusoids, each sinusoid having a signal amplitude and a signal phase;
estimating the signal amplitude and the signal phase for each sinusoid in the frequency grid;
computing an average background power level; and
detecting signals with power higher than the average background power level;
wherein the non-uniform sampling interval varies predictably;
wherein the non-unifoun sampling interval is a function of the average time step, the variation size, and a ratio of a current sample number relative to a total number of samples taken;
wherein the non-uniform sampling interval is defined by:
Δ
t
n
=
dt
(
1
-
f
+
2
f
n
n
max
)
wherein n is the current sample number having a sampling interval Δt n , dt is the average time step, f is the variation size, and n max is the total number of samples.
8. The method of claim 7 , wherein the non-uniform sampling interval increases linearly.
9. The method of claim 7 , wherein the non-uniform sampling interval has a step size that varies within specified minimum and maximum values.
10. The method of claim 7 , wherein the variation size f has a value of 0.5.
11. The method of claim 7 , wherein the total number of samples n max has a value that is an integer multiple of 512.
12. The method of claim 7 , wherein detecting the signals with the power higher than the average background power level comprises finding one frequency at a time that has a highest power.
13. The method of claim 7 , wherein detecting the signals with the power higher than the average background power level comprises finding a maximum frequency and a shape of a power spectral distribution (P SD) near the maximum frequency and using the PSD to detect a portion of the signals that best matches a PSD template.
14. The method of claim 7 , further comprising:
removing the signals with the power higher than the average background power level from the sampled received signal; and
repeating the mapping, estimating, computing, and detecting operations.
15. The method of claim 7 , wherein the average time step dt is less than or equal to ten times a Nyquist sampling time.
16. A system comprising:
a receiver front-end configured to receive a wideband signal;
a signal generator configured to generate a sampling signal with a non-uniform sampling interval having an average time step with a variation size;
an analog-to-digital converter (ADC) configured to sample the received wideband signal using the sampling signal; and
at least one processing device configured to:
map the sampled received signal onto a frequency grid of sinusoids, each sinusoid having a signal amplitude and a signal phase;
estimate the signal amplitude and the signal phase for each sinusoid in the frequency grid;
compute an average background power level; and
detect signals with power higher than the average background power level;
wherein the non-uniform sampling interval varies predictably;
wherein the non-uniform sampling interval is a function of the average time step, the variation size, and a ratio of a current sample number relative to a total number of samples taken;
wherein the non-uniform sampling interval is defined by:
Δ
t
n
=
dt
(
1
-
f
+
2
f
n
n
max
)
wherein n is the current sample number having a sampling interval Δt n , dt is the average time step, f is the variation size, and n max is the total number of samples.
17. The system of claim 16 , wherein the at least one processing device is further configured to:
remove the signals with the power higher than the average background power level from the sampled received signal; and
repeat the map, estimate, compute, and detect operations.
18. The system of claim 16 , wherein the non-uniform sampling interval increases linearly.
19. The system of claim 16 , wherein the non-uniform sampling interval has a step size that varies within specified minimum and maximum values.
20. The system of claim 16 , wherein:
the variation size f has a value of 0.5;
the total number of samples n max has a value that is an integer multiple of 512; and
the average time step dt is less than or equal to ten times a Nyquist sampling time.