Method and system for down-converting and up-converting an electromagnetic signal, and transforms for same

• US 7,308,242 B2
• Filed: 08/10/2004
• Issued: 12/11/2007
• Est. Priority Date: 10/21/1998
• Status: Expired due to Term

• Current Assignee: ParkerVision, Inc.
• Original Assignee: ParkerVision, Inc.
• Inventors: Sorrells, David F., Bultman, Michael J., Cook, Robert W., Looke, Richard C., Moses, Charley D. Jr., Rawlins, Gregory S., Rawlins, Michael W.
• Primary Examiner(s): Trinh, Sonny
• Application Number:
  US10/914,337
• Publication Number:
  US 20050009494A1
• Time in Patent Office: 1,218 Days
• Field of Search: 455/313, 455/323, 455/190.1, 455/112, 455/131, 455/327, 455/333, 455/118, 455/130, 455/76, 455/91, 455/260, 455/191.1, 455/182.1, 375343-344, 375/350, 327/100, 327/113
• US Class Current: 455/313
• CPC Class Codes: H03C 1/62 Modulators in which amplitude of carrier component in output is dependent upon strength of modulating signal, e.g. no carrier output when no modulating signal is present H03C1/28 - H03C1/34, H03C1/46, H03C1/48 take precedence
• CPC Class Codes: H03D 7/00 Transference of modulation from one carrier to another, e.g. frequency-changing H03D9/00, H03D11/00 take precedence; dielectric amplifiers, magnetic amplifiers, parametric amplifiers used as a frequency-changers H03F
• CPC Class Codes: H04B 7/12 Frequency diversity

Abstract

Methods, systems, and apparatuses, and combinations and sub-combinations thereof, for down-converting and up-converting an electromagnetic (EM) signal are described herein. Briefly stated, in embodiments the invention operates by receiving an EM signal and recursively operating on approximate half cycles (½, 1½, 2½, etc.) of the carrier signal. The recursive operations can be performed at a sub-harmonic rate of the carrier signal. The invention accumulates the results of the recursive operations and uses the accumulated results to form a down-converted signal. In an embodiment, the EM signal is down-converted to an intermediate frequency (IF) signal. In another embodiment, the EM signal is down-converted to a baseband information signal. In another embodiment, the EM signal is a frequency modulated (FM) signal, which is down-converted to a non-FM signal, such as a phase modulated (PM) signal or an amplitude modulated (AM) signal. Up-conversion is accomplished by controlling a switch with an oscillating signal, the frequency of the oscillating signal being selected as a sub-harmonic of the desired output frequency.

Claims

1. A method for down-converting a signal comprising:

(a) recursively applying a matched filter operation to said signal at a rate sub-harmonically related to said signal;

(b) retaining and accumulating a result of said matched filter operation to provide an initial condition for subsequent recursions of said matched filter operation, wherein said accumulation is approximated as a zero order data hold filter; and

(c) generating a down-converted signal from said accumulated results.

2. The method of claim 1, wherein step (a) comprises multiplying said signal by itself over a time interval defined for said signal, and then integrating the result over said time interval.

3. The method of claim 2, further comprising acquiring sampling information from energy under a half sine curve, wherein said energy under said half sine curve is proportional to a peak of said signal.

4. The method of claim 1, further comprising acquiring energy from said signal under a half-sine cycle, thereby minimizing effects of aperture uncertainty.

5. The method of claim 1, wherein step (a) is performed with a single aperture RC processor that is a first order approximation of said matched filter operation, where a pulse shape being matched is a half-sine pulse.

6. The method of claim 5, wherein said RC processor integrates across an acquisition aperture and stores the result to accumulate said result with a subsequent aperture.

7. The method of claim 6, wherein a maximum voltage is accumulated by said RC processor at time t≅

0.75T_A and β

≅

2.6, wherein the forcing function is a half sine pulse, T_A is the aperture duration and β

=(RC)<sup>−

1</sup>.

8. The method of claim 7, wherein when said RC processor accumulates charge over multiple apertures and wherein signal to noise ratio (SNR) and charge transfer is optimized for β

≈

0.25, and T_A≈

1.

9. The method of claim 7, wherein said signal has frequency ƒ

_c related to aperture duration T_A by ƒ

_c≈

(2T_A)<sup>−

1</sup>.

10. The method of claim 7, wherein said aperture having a ratio of

$\frac{T_A}{T_c}=\frac{1}{2},$

results in an optimal design parameter for a low DC offset system, wherein T_c is a period of said signal.

11. The method of claim 6, wherein said RC processor calculates a numerical result substantially similar to that of an ideal sampler by averaging over multiple apertures.

12. The method of claim 11, wherein said RC processor aperture design produces results similar to that of an impulse sampler, scaled by a gain constant, and possesses lesser variance than an impulse sampler.

13. The method of claim 6, wherein said RC processor reduces the variance of an expected ideal sample, over that obtained by impulse sampling, by averaging over multiple apertures.

14. The method of claim 13, wherein an impulse sampler value expected at time T_A/2 is derived by said RC processor operating over an aperture of duration T_A.

15. The method of claim 6, wherein a clock signal controlling said aperture of said RC processor is defined as:

$\begin{array}{c}{C}_I<br><br>\left(t\right)=<br><br>\underset{m=-\mathrm{\infty <br><br>}}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br><br><br>\mathrm{\delta <br><br>}<br><br>\left(t-{\mathrm{mT}}_S\right)*p_C<br><br>\left(t\right)=\underset{m=-\mathrm{\infty <br><br>}}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br><br><br>p<br><br>\left(t-{\mathrm{mT}}_S\right)\\ C_I<br><br>\left(t\right)=<br><br>\underset{m=-\mathrm{\infty <br><br>}}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\left(u<br><br>\left(t\right)-u<br><br>\left(t-T_A\right)\right)*\mathrm{\delta <br><br>}<br><br>\left(t-{\mathrm{mT}}_S\right)\\ C_Q<br><br>\left(t\right)=<br><br>\underset{m=-\mathrm{\infty <br><br>}}{\overset{\mathrm{\infty <br><br>}}{\sum <br><br>}}<br><br>\left(u<br><br>\left[t-T_A/2\right]-u<br><br>\left[t-3<br><br>T_A/2\right]\right)*\mathrm{\delta <br><br>}<br><br>\left(t-\left({\mathrm{mT}}_S+T_A/2\right)\right)\end{array}$

wherein,

C_I(t) is a complex in phase clock shifted in phase by T_A/2,

C_Q(t) is a complex quadrature phase clock shifted in phase by T_A/2,

P_c(t)Δ

is a basic pulse shape of said clock (gating waveform) having correlation properties matched to a half sine of said signal,

T_sΔ

is a time between recursively applied gating waveforms,

T_AΔ

is an aperture duration, and

δ

(t)Δ

is an impulse sample function.

16. The method of claim 6, wherein an optimal capacitance (C_s) for said RC processor is related to said aperture width (Aperture_Width), a resistance (R) and frequency of apertures (ƒ

reqLO) by the equation

$C_s<br><br>\left(R\right)=\left(\frac{\frac{1}{\mathrm{freqLO}}-\mathrm{Aperture\_Width}}{-\ln <br><br>\left(0.841\right)·<br><br>R}\right).$

17. The method of claim 5, further comprising:

successively applying said matched filter operation of said RC processor on said signal at a rate;

f_s=f_c/M

wherein,

f_sΔ

is a sampling rate,

f_cΔ

is a signal frequency, and

MΔ

is an integer such that 0<

M<

∞

.

18. The method of claim 17, wherein M is greater than or equal to 3 and lesser than or equal to 10.

19. The method of claim 17, wherein said sampling rate is greater than twice an information bandwidth frequency of said signal.

20. The method of claim 17, wherein a ratio of said sampling rate (ƒ

_s) to number of samples (l) is greater than an information bandwidth frequency of said signal.

21. The method of claim 20, wherein voltage accumulated per microsecond (V_μ

sec) is

$V_{\mathrm{\mu <br><br>}<br><br><br><br>\sec }\cong <br><br>l_s<br><br>\frac{A^2<br><br>T_A}{2}$

wherein,

l_s is a number of samples accumulated per microsecond, and

A is an amplitude of an original component of a complex modulation envelope for said signal.

22. The method of claim 1, wherein a maximum output of said matched filter operation occurs when said signal and a corresponding aperture are substantially overlapped for a time observation t₀≈

T_A.

23. The method of claim 1, wherein said matched filter comprises a correlator that acquires substantially all of the energy available across a finite duration aperture.

24. The method of claim 1, wherein energy accumulated over an aperture is

$E_l={\int }_{}^{}$

0 T A ⁢

S i 2 ⁡

( t ) ⁢

ⅆ

t = A n 2 ⁢

T A 2

wherein,

A_nΔ

is a carrier signal envelope weighting of the nth sample, and

S_i(t) is the original signal.

25. The method of claim 1, wherein step(a) comprises multiplying said signal by itself over a time interval defined for said signal, wherein step(b) comprises integrating the result of step(a) over said time interval according to:

∫

<sub>−

0</sub>^TAS_i²(t)dt

wherein,

S_i(t) is the original signal, and

T_A is an aperture duration.