Apparatuses and methods for linear to discrete quantization conversion with reduced sampling-variation errors
Provided is an apparatus for converting a continuous-time, continuously variable signal into a sampled and quantized signal, which includes an input line for accepting an input signal, multiple processing branches coupled to the input line, and an adder coupled to outputs of the plurality of processing branches. Each of the processing branches includes a sampling/quantization circuit and a digital bandpass interpolation filter having an input coupled to an output of the sampling/quantization circuit. The digital bandpass interpolation filters in different ones of the processing branches have frequency responses that are centered at different frequencies. The digital bandpass interpolation filter in at least one of the processing branches includes: (i) a quadrature downconverter, (ii) a first lowpass filter and a second lowpass filter, (iii) a first interpolator and a second interpolator, each having an input for inputting a variable interpolant value, and (iv) a quadrature upconverter.
1. An apparatus for fabricating new discrete-time data samples from existing discrete-time data samples, comprising:
an input line for accepting an input signal;
a plurality of processing branches coupled to the input line, each of said processing branches including: (a) a branch input coupled to the input line and inputting input samples that are discrete in time and value; (b) a downconverter, having an input coupled to the branch input, that uses sine and cosine sequences to convert an intermediate-frequency input into complex-valued data samples represented by quadrature baseband and in-phase baseband outputs, (c) a first lowpass filter coupled to the quadrature baseband output of the downconverter; (d) a second lowpass filter coupled to the in-phase baseband output of the downconverter; (e) a first interpolator coupled to an output of the first lowpass filter, (f) a second interpolator coupled to an output of the second lowpass filter, and (g) a quadrature upconverter that uses sine and cosine sequences to convert complex-valued data samples represented by baseband outputs of the first and second interpolators into an intermediate-frequency output; and
an adder coupled to outputs of the plurality of processing branches,
wherein different ones of the plurality of processing branches operate at different intermediate frequencies,
wherein a phase rotation, in an amount based on a variable interpolant value, is applied to complex-valued data samples originating from the downconverter, and
wherein the input samples and output samples of at least one of the plurality of processing branches are different discrete-time representations of an underlying continuous-time signal, with the output samples representing an altered sampling period, as compared to the input samples, and with the sampling period being altered by an amount that depends on the variable interpolant value.
2. An apparatus according to claim 1 , further comprising:
a sampling error estimator having an output coupled to at least one of said processing branches,
wherein the output of the sampling error estimator has a value which is proportional to fluctuations in a nominal oscillation period of a signal provided to an input of the sampling error estimator, and
wherein the output of the sampling error estimator is used by at least one of said processing branches to fabricate new data samples from existing data samples.
3. An apparatus according to claim 1 , further comprising:
a resampling data buffer coupled to the output of at least one of said processing branches,
wherein the resampling data buffer receives data samples at a first time interval that is different from a second time interval at which the resampling data buffer delivers data samples.
4. An apparatus according to claim 1 , wherein at least one of the first lowpass filter and the second lowpass filter in at least one of the processing branches incorporates a recursive moving-average operation.
5. An apparatus according to claim 1 , wherein at least one of said processing branches also includes an equalizer, disposed between the downconverter and the quadrature upconverter, having a least one complex tap.
6. An apparatus according to claim 5 , wherein the equalizer has plural complex taps.
7. An apparatus according to claim 1 , wherein the sine and cosine sequences used by the downconverter and the quadrature upconverter in at least one of the processing branches are generated using a direct digital synthesis method that employs digital accumulators and phase lookup tables.
8. An apparatus according to claim 1 , wherein the sine and cosine sequences used by the downconverter and the quadrature upconverter in at least one of the processing branches are generated using recursive operations.
9. An apparatus according to claim 1 , wherein at least one of the sine and cosine sequences used by at least one of the downconverter and the quadrature upconverter is adjustable in at least one of amplitude or phase.
10. An apparatus according to claim 1 , wherein the plurality of processing branches operate at center frequencies that are spaced at equal frequency intervals.
11. An apparatus according to claim 10 , wherein the plurality of processing branches operate at center frequencies that are spaced at non-equal frequency intervals.
12. An apparatus according to claim 1 , wherein the input signal is continuous in time and value, and the plurality of processing branches are coupled to the input line via at least one sampling/quantization circuit.
13. An apparatus according to claim 1 , wherein the input signal is continuous in time and value, and the plurality of processing branches are coupled to the input line via at least one sampling/quantization circuit and at least one analog bandpass filter.
14. An apparatus according to claim 1 , wherein an interpolation operation performed by at least one of the interpolators is based on a second-order function.
15. An apparatus according to claim 1 , wherein the interpolation operation performed by at least one of the interpolators is based on a first-order function.
16. An apparatus for digitally processing a discrete-time signal, comprising:
an input line for accepting an input signal;
a plurality of processing branches coupled to the input line, each of said processing branches including: (a) a branch input coupled to the input line and inputting input samples that are discrete in time and value; (b) a downconverter, having an input coupled to the branch input, that uses sine and cosine sequences to convert an intermediate-frequency input into complex-valued data samples represented by quadrature baseband and in-phase baseband outputs, (c) a first baseband processor coupled to the quadrature baseband output of the downconverter; (d) a second baseband processor coupled to the in-phase baseband output of the downconverter; and (e) a quadrature upconverter that uses sine and cosine sequences to convert complex-valued data samples represented by baseband outputs of the first and second baseband processors into an intermediate-frequency output; and
an adder coupled to outputs of the plurality of processing branches,
wherein different ones of the plurality of processing branches operate at different intermediate frequencies,
wherein each of said baseband processors includes: (a) a first lowpass filter coupled to an output of the downconverter, (b) a downsampling circuit that subsamples the output of the first lowpass filter, (c) an upsampling circuit that increases the sampling rate at the output of the downsampling circuit, and (d) a second lowpass filter coupled to the output of the upsampling circuit,
wherein each of said first and second lowpass filters have a frequency response which decreases in magnitude versus frequency according to a function that is approximately sin(x)/x, and
wherein the bandpass responses of said processing branches combine to form an all-pass response that distorts amplitude and phase of the input signal by less than 5%.
17. An apparatus according to claim 16 , wherein said quadrature upconverter utilizes a quadrature multiplier to shift baseband outputs of said first and second lowpass filters to a center frequency other than zero hertz, and wherein the outputs of said first and second lowpass filters are combined to form a real output signal.
18. An apparatus according to claim 16 , wherein said quadrature upconverter utilizes a complex multiplier to shift baseband outputs of said first and second lowpass filters to a center frequency other than zero hertz, and wherein the outputs of said first and second lowpass filters are combined to form a complex output signal represented by in-phase and quadrature components.
19. An apparatus according to claim 16 , wherein said downconverter utilizes a quadrature multiplier to convert a real-valued input signal into a baseband output having in-phase and quadrature components.
20. An apparatus according to claim 16 , wherein said downconverter utilizes a complex multiplier to convert a complex-valued input signal, represented by in-phase and quadrature components, into a baseband output having in-phase and quadrature components.
21. An apparatus according to claim 16 , wherein at least one of the said baseband processors includes a polynomial interpolation function which, according to a variable interpolant value, fabricates an estimated data sample from actual data samples.
22. An apparatus according to according to claim 21 , wherein said polynomial interpolation function is based on a second-order function.
23. An apparatus according to according to claim 21 , wherein said polynomial interpolation function is based on a first-order function.
24. An apparatus according to claim 16 , wherein at least one of the said baseband processors includes a phase rotation function, which, in an amount based on a variable interpolant value, modulates the phase of complex-valued data samples originating from the quadrature downconverter.
25. An apparatus according to claim 16 , wherein at least one of the first lowpass filter and the second lowpass filter in at least one of the baseband processors incorporates a moving-average operation.
26. An apparatus according to according to claim 16 , wherein at least one of said baseband processors also includes an equalizer, having a least one complex tap.
27. An apparatus according to claim 26 , wherein the equalizer has plural complex taps.
28. An apparatus according to according to claim 16 , wherein the sine and cosine sequences used by the downconverter and the quadrature upconverter in at least one of the processing branches are generated using a direct digital synthesis method that employs digital accumulators and phase lookup tables.
29. An apparatus according to according to claim 16 , wherein the sine and cosine sequences used by the downconverter and the quadrature upconverter in at least one of the processing branches are generated using recursive operations.
30. An apparatus according to according to claim 16 , wherein at least one of the sine and cosine sequences used by at least one of the downconverter and the quadrature upconverter is adjustable in at least one of amplitude or phase.
31. An apparatus according to according to claim 16 , wherein the plurality of processing branches operate at center frequencies that are spaced at equal frequency intervals.
32. An apparatus according to according to claim 16 , wherein the plurality of processing branches operate at center frequencies that are spaced at non-equal frequency intervals.