Digital to analog conversion using non-uniform sample rates

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to the field of methods and circuits for digital to analog conversion. More particularly, the present invention relates to a method and circuit for digital to analog signal conversion using sigma-delta modulation of the temporal spacing between digital samples.

2. Discussion of the Related Art

Digital to Analog Converter (DAC) circuits and methods for digital to analog conversion are well-known in the art. Conventional DACs receive a binary level single or multi-bit digital signal on an input terminal(s) and, as a function of a reference voltage, convert the digital signal into a corresponding analog signal.

One type of DAC that has recently become popular is the so-called sigma-delta DAC. There are many references describing sigma-delta systems. One example is entitled Mixed-Signal Design Seminar published by Analog Devices, Inc., 1991, which is incorporated herein by reference.

As shown in FIG. 1, a conventional sigma-delta digital to analog converter includes an interpolation filter 1 that increases the sample rate (i.e. data rate or sampling frequency) of a digital input signal by some predetermined oversampling ratio to a higher sampling rate and rejects any signal images that occur at approximately the Nyquist rate of the input signal. The higher rate digital signal is then transmitted to a sigma-delta modulator 2 that noise shapes the digital data stream and reduces the sample width to one bit. In digital to analog converters, the sigma-delta modulator is typically all digital. The sigma-delta modulator effectively low pass filters the signal of interest and high pass filters the quantization noise on the signal. The output of the sigma-delta modulator is typically a high frequency one-bit data stream. The one-bit DAC 3 receives the modulator output and provides a corresponding analog signal that is either plus or minus full scale. The output of the one-bit DAC is transmitted to an analog smoothing filter 4 that averages the output of the one-bit DAC and removes the shaped quantization noise that resides in the upper frequency area.

One of the limitations of conventional DACs including the sigma-delta DAC illustrated in FIG. 1 is that they only determine the magnitude of the input signal at equally spaced temporal intervals. This is known as uniform sampling. Additionally, in conventional DACs, the sample rate, that is, the data rate of the incoming digital data stream cannot be independent of the master clock that is used to clock the DAC. The incoming digital data rate must be some integer division of the master clock on the DAC chip. This means that if the DAC were to receive digital data at two different data rates, that are not necessarily divisible into the master clock (or more generally, digital data at a rate that is not integrally divisible into the master clock), there must be two different frequency master clocks available for clocking the DAC (or more generally, there must be a master clock that has an integer relationship with the data rate of the incoming digital data available to clock the DAC).

Another problem with conventional DACs is that they typically are not designed to be clocked by an externally supplied clock signal. The components of the DAC are typically optimized to operate at the clock frequency determined by the master clock on the DAC chip. This leads to the additional limitation that some DACs cannot lock to and operate at some externally supplied clock signal. Therefore, if there are any changes in the digital data rate, since the incoming digital data stream and the master clock for the DAC are not necessarily related to each other, any changes in the relative frequencies of the data rate and the master clock can disrupt the entire digital to analog conversion process.

Therefore, an object of the present invention is to provide a method and apparatus for performing digital to analog conversion using non-uniform sampling (i.e., variable temporal spacing of the sampling points).

Another object of the present invention is to provide a method and apparatus for performing digital to analog conversion that can lock to an externally supplied clock signal and can provide a sampling rate that is independent of the DAC master clock.

SUMMARY OF THE INVENTION

The present invention overcomes the limitations of the prior art by providing a method and apparatus for digital to analog conversion using non-uniform sampling. The apparatus includes an interpolator or other comparable circuitry such as a sample and hold circuit for receiving digital signals at a first data rate and for supplying the digital signals at an increased data rate and a decimator, coupled to the interpolator, for decimating the digital signals at the increased data rate to provide digital signals at a second data rate. In one embodiment, a sigma-delta modulator is coupled to and controls the decimator and provides a sigma-delta modulated output signal representative of the first data rate and controls the decimator to provide the digital signals at the second rate. This embodiment of the invention interpolates digital data by a fixed ratio and then decimates the interpolated digital data by a variable ratio depending on the second data rate desired. A digital to analog converter is coupled to and receives the digital signals at the second data rate from the decimator and converts the digital signals at the second data rate to analog signals.

In another embodiment of the invention, a phase locked loop (PLL) which may be a digital or analog PLL is provided for receiving a signal representative of the first data rate, locking to the signal, and providing a control signal to the sigma-delta modulator that controls the sigma-delta modulator to provide the sigma-delta modulated output signal. The sigma-delta modulator forms part of the digitally controlled oscillator in the PLL. The phase locked loop allows the circuit to lock to and track any externally-supplied clock signal.

Broadly stated, the method of the present invention includes sigma-delta modulation of the time base such that errors produced by non-uniform sampling are frequency-shaped to a region (i.e., shifted to higher frequencies) where they can be removed by conventional filtering techniques.

In one embodiment of the invention, the method is to perform a fixed interpolation (or other method of increasing the data rate of the digital signal) and filtering to remove images followed by variable decimation with the decimation controlled by a sigma-delta modulator that is fed a frequency selection signal representing the sampling frequency of the input data stream. Fixed interpolation means that the interpolation ratio is the same regardless of the sample rate. Variable decimation means that the decimation ratio is varied as a function of the desired output sample rate. A digital data stream at a data rate within some predetermined limits is interpolated to a higher data rate. This higher data rate digital data stream is then decimated using a control signal that is a sigma-delta modulated signal that represents the data rate of the incoming digital data stream. The frequency selection signal is modulated using an n-th order m-bit sigma-delta modulator. This control signal (the sigma-delta modulated frequency selection number output by the sigma-delta modulator) represents, on average, the data rate of the incoming digital data stream. Data thus emerges from the interpolation/decimation process at the clock rate of the n-th order m-bit sigma-delta modulator.

The method thus converts the data rate of the incoming digital data stream to the data rate of the n-th order m-bit sigma-delta modulator.

The features and advantages of the present invention will be more readily understood and apparent from the following detailed description of the invention, which should be read in conjunction with the accompanying drawings, and from the claims which are appended at the end of the detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings, which are incorporated herein by reference and in which like elements have been given like reference characters,

FIG. 1 is a block diagram of a conventional sigma-delta digital to analog converter (DAC);

FIG. 2 is a block diagram of a general DAC circuit incorporating one embodiment of the invention;

FIG. 3 is a block diagram of a sigma-delta DAC circuit incorporating one embodiment of the invention;

FIG. 4 is a more detailed block diagram of the circuit of FIG. 3;

FIG. 5 is a block diagram of a circuit for supplying previously stored frequency numbers to the n-th order m-bit sigma-delta modulator of FIGS. 2-4 and 7-9; and

FIG. 6 is a block diagram of a locking circuit that may be used in conjunction with the circuits of FIGS. 2-4 to lock the DAC to an externally supplied clock signal; and

FIG. 7 is a flow chart illustrating the steps of the method of the invention using fixed interpolation followed by variable decimation.

DETAILED DESCRIPTION

For purposes of illustration only, and not to limit generality, the present invention will now be explained with reference to specific data rates, interpolation (or more generally sample rate increase) ratios, decimation ratios, and clock frequencies of operation. One skilled in the art will recognize that the present invention is not limited to the specific embodiment disclosed, and can be more generally applied to other circuits and methods having different operating parameters than those illustrated.

FIG. 2 is a block diagram broadly illustrating the invention. The overall purpose of circuit 10 is to receive a digital data stream on line 12 at any data rate within a predetermined working range of the system, increase the sampling rate of the data stream and then decimate this higher rate data stream so that the data stream presented on line 14 is at a fixed, predetermined data rate. In other words, circuit 10 receives digital data at any data rate within the predetermined working range of the system, and converts this data to a digital data stream at another data rate. The other data rate may or may not be the same as the data rate of the input data stream and may be a fixed or a variable rate. The digital data stream on line 12 may be of any width.

In the circuit illustrated in FIG. 2, an interpolator 16 receives the digital data stream on line 12 at any data rate within the predetermined working range. Interpolator 16 increases the sample rate of the digital data stream (that is, converts the digital data stream into a higher sample rate digital data stream) on line 12 by, for example, inserting zeros between data samples, in a manner well-known to those skilled in the art. One skilled in the art will appreciate that other techniques may be used for increasing the sample rate of the data stream on line 12, such as sample and hold techniques. A higher sample rate digital data stream 17 is then sent to a digital filter 18 which removes any images of the original digital signal as a result of the interpolation process. The filtered digital data stream on line 19 is then sent to a decimation block 21 that decimates digital data stream on line 19 under control of the sigma-delta modulator 20. Although filter 18 and decimation block 21 have been illustrated as separate circuit elements for illustrative purposes, one skilled in the art will appreciate that these functions may be performed by a single computational element, such as an FIR or IIR filter in a well-known manner.

The sigma-delta modulator 20 produces digital data at the frequency of clock 22, the data controlling the decimation of decimation block 21. As will be explained in more detail hereinafter, the sigma-delta modulator 20 sigma-delta modulates a signal 24 representative of the data rate of the digital data stream on line 12. An example will serve to illustrate this function. Assume that the data rate of the data stream on line 12 is 48 kHz. Interpolator 16 increases this data rate to 18.432 MHz by interpolating the data by a factor of 384. Assume the frequency of clock 22 is 3.072 MHz. Since the data rate of data stream 12 is 48 kHz, signal 24 is therefore a multi-bit digital number representative of a sampling rate of 48 kHz where the number of bits in the digital number control the precision with which the data rate of digital data stream on line 12 can be specified. This digital number is sigma-delta modulated by the sigma-delta modulator 20 and used to control decimation block 21 to produce one output signal for every six samples in digital data stream 19. The 18.432 MHz data is then effectively decimated by a factor of six and the digital data stream on line 14 is therefore at, on average, a 3.072 MHz data rate.

Sigma delta modulator 20 is preferably an n-th order m-bit sigma-delta modulator. The higher the order of the sigma-delta modulator, the better the noise shaped characteristics of the output signal on line 26. The output signal on line 26 of sigma-delta modulator 20 is chosen to be m-bits (where m.gtoreq.1 and is more than one bit in a preferred embodiment) because, as the number of bits is increased, the clock rate necessary to operate sigma-delta modulator 20 can be reduced. However, it is to be appreciated that the invention is not so limited. Sigma-delta modulator 20 could also be a one bit modulator if the clock frequency used to run the modulator is appropriately increased.

A key feature of the present invention is that the temporal spacing of the sampling points is controlled by the n-th order m-bit sigma-delta modulator such that any errors (i.e., noise on the sampling points) produced by this non-uniform sampling are shaped in the frequency domain. As is well-known in the field of sigma-delta systems, this error produced by noise resulting from the non-uniform sampling can be removed by conventional digital filtering techniques.

Several other advantages are also obtained. By appropriate choice of the rate at which the sigma-delta spaced sampling points are generated and the number of bits used in controlling the spacing of these sampling points, the signal to noise ratio of the digital data stream on line 14 can be controlled. Further degrees of freedom are available by varying the order of the sigma-delta modulator used to control the sampling points. In another aspect of the invention, the degree of filtering used on the digital data stream on line 17 can also be varied to vary the signal to noise ratio as well.

As shown in FIG. 2, the output data stream on line 14 is fed into a DAC 28 which may be any well-known type of digital to analog converter to produce an analog output signal on line 36.

FIG. 3 illustrates a sigma-delta DAC 98 using the present invention. In FIG. 3, digital data stream on line 14 is fed into a sigma-delta modulator 30, digital to analog converter 32, and an analog smoothing filter 34 to produce an analog output signal on line 36. Sigma delta modulator 30, digital to analog converter 32, and analog smoothing filter 34 are similar to those illustrated in FIG. 1 and are well-known to those skilled in the art and therefore will not be discussed in further detail herein.

FIG. 4 illustrates a more detailed embodiment of the DAC of FIG. 3. In the embodiment 100 of FIG. 4, an n-bit wide digital data stream on line 50 which may be, for example, in the range of 4 kHz to 48 kHz is received by interpolator 52. Interpolator 52 increases the sample rate of digital data stream on line 50 by a factor of four using, for example, a zero fill technique that inserts zeros between the digital samples. The higher sample rate signal output by interpolator 52 (now in the range of 16 kHz to 192 kHz) is then fed into a digital low pass filter 54 which may be, for example, a finite impulse response type filter. Low pass filter 54 filters out of band images of digital signal 50 out of the digital data stream on line 53. The filtered digital data stream on line 56 from low pass filter 54 is then fed into interpolator 58 that increases the sample rate of the digital data stream on line 56 by a factor of ninety-six. Inserting ninety-five zeros into the digital data stream on line 56 will reduce the gain of the original signals because of the dilution of the signal by the inserted zeros. However, as is well-known, the parameters of filter 62 can be adjusted to compensate for this loss of gain. The higher sample rate digital data signal on line 60 (now in the range of 1.536 MHz to 18.432 MHz) provided by interpolator 58 is fed into digital filter 62.

As stated previously, other techniques, such as sample and hold techniques, may be used to increase the sample rate in place of interpolators 52, 58. The use of a sample and hold technique is advantageous because it automatically compensates for the energy lost in creating the images of the original signal due to the interpolation process.

In one embodiment, digital filter 62 is a sinc 96.sup.4 -type filter that is designed to have zeros at the image frequencies of the digital data stream on line 60. Filter 62 could, however, be any type of IIR or FIR filter. In the preferred embodiment illustrated in FIG. 4, digital filter 62 provides both a low pass filtering function and a decimation function. One skilled in the art will appreciate that these two functions could be separated in the manner illustrated in FIGS. 2 and 3. As will be explained in greater detail hereinafter, filter 62 outputs a digital data stream on line 64 at 3.072 MHz. The digital data stream on line 64 is input to a sigma-delta modulator 66 that is clocked at 3.072 MHz. Sigma-delta modulator 66 could also be an n-th order m-bit modulator similar to sigma-delta modulator 78. Sigma delta modulator 66 outputs a single-bit data stream on line 68 that is fed into digital to analog converter 70. The analog signal on line 72 output by digital to analog converter 70 is fed through smoothing filter 74 to produce a final analog output signal on line 76.

It is to be noted that the digital data streams on lines 53, 56, 60, and 64 are indicated as being n-bits wide in FIG. 4. N may be any number of bits and is typically chosen to be the widest bit stream commensurate with the signal-to-noise ratio requirements of the particular application. Furthermore, the digital data streams may be different widths on each of the lines.

The n-th order m-bit sigma-delta modulator 78 provides a four-bit number on line 80 that controls filter 62 to produce the output data stream on line 64. Sigma-delta modulator 78 is, in one embodiment, a fourth order four-bit modulator. Sigma delta modulator 78 is also clocked using a 3.072 MHz clock.

In one embodiment, a twenty-bit frequency selection number 82 is input into sigma-delta modulator 78. Frequency selection number 82 ranges from -2.sup.19 to +2.sup.19. This twenty-bit number controls the precision with which the four-bit number output by sigma-delta modulator 78 represents the sampling rate of the input digital data stream on line 50. Sigma-delta modulator 78 modulates the twenty-bit number to produce sigma-delta modulated four-bit codes that control filter 62. The first bit of the code is a sign bit. The remaining three bits produce codes that direct the filter 62 to calculate and produce an output every P samples of data stream on line 60, effectively sample rate converting the data stream.

Table 1 illustrates the relationship among the four-bit codes that are produced by sigma-delta modulator 78, the intervals at which filter 62 produces an output, and the sampling frequency that the four-bit code corresponds to when modulator 78 is clocked using a 3.072 MHz clock. Some examples will illustrate the operation of the system.

TABLE 1 ______________________________________ PRODUCE AN CORRESPONDING OUTPUT EVERY TO SAMPLING 4 BIT CODE P SAMPLES FREQUENCY OF (KHZ) ______________________________________ +4 8 64 +3 7 56 +2 6 48 +1 5 40 0 4 32 -1 3 24 -2 2 16 -3 1 8 -4 0 DC ______________________________________

Assume, for purposes of illustration, that the digital data stream on line 50 has a data rate of 48 kHz. Interpolator 52 increases this data rate to 192 kHz. Interpolator 58 increases the 192 kHz sampling rate to 18.432 MHz. To produce the digital data stream on line 64 at 3.072 MHz at the output of filter 62, the digital data stream on line 60 at 18.432 MHz must be decimated by a factor of six. Therefore, twenty-bit frequency selection number 82 is selected such that upon sigma-delta modulation by the fourth order four-bit sigma-delta modulator 78, the four bit codes generated will be, on average, a +2 code although other four bit codes will be produced but with a lower frequency of occurrence.

A key point to remember is that the +2 code is the resulting average of all the codes produced by sigma-delta modulator 78 upon sigma-delta modulation of twenty-bit frequency selection number 82. A +2 code is not produced every time sigma-delta modulator 78 is clocked even though the input and output sample rate are related to each other by an integer multiple. Even if the sample rates were related to each other by an integer multiple, any errors, no matter how small, that result in a temporal displacement between the sample points in the input digital data stream on line 50 and the sample points in the rate-converted digital data stream on line 64 would increase the signal to noise ratio to a point where the digital to analog conversion process would not be acceptable. In the present invention, the time base (i.e., the temporal spacing between samples) is sigma-delta modulated so that the errors due to temporal displacement between the input and rate-converted digital data stream that cause noise are pushed into a higher frequency range. This noise is then removed by conventional filtering techniques such as in analog smoothing filter 34.

As shown in Table 1, the +2 (on average) code directs filter 62 to produce an output every six data samples of digital data stream on line 60. This results in the output data stream on line 64 having a data rate (i.e., a sample rate or sampling frequency) of 3.072 MHz on average.

In another example, assume that the digital data stream on line 50 has a data rate (i.e., a sample rate or sampling frequency) of 4 kHz. Interpolator 52 increases this data rate to 16 kHz. Interpolator 58 increases the 16 kHz data rate to 1.536 MHz. In order that the digital data stream on line 64 have a data rate of 3.072 MHz, the digital data stream on line 60 at 1.536 MHz must be effectively interpolated by a factor of 2. Therefore twenty-bit frequency selection number 82 is chosen such that sigma-delta modulator 78 produces, on average, an equal number of -3 and -4 codes although other four bit codes will be produced, but with a lower frequency of occurrence. That is, occasionally, -2, -1, and even less frequently, +1, +2 codes will be produced. As shown in Table 1, the -3 code directs sinc filter 62 to produce an output for each input sample corresponding to a sampling frequency of 8 kHz for the clock frequencies and interpolation ratios illustrated.

The -4 code is used to control filter 62 so that it does not produce a new output but rather repeats the previous output. That is, the filter 62 is directed to produce an output, but since a new data point has not been received and the previous data point is still at the filter input, the filter 62 repeats the calculation and produces the same output again.

At the illustrated interpolation ratios and clock frequencies, the -3 code represents a sampling frequency of 8 kHz and the -4 code represents a sampling frequency of DC (i.e., no signal). Therefore, on an average of many samples, the -3 and -4 four-bit codes produce a sampling frequency of 4 kHz to provide a digital data stream on line 64 at 3.072 MHz.

One skilled in the art will appreciate that any sampling frequencies within the 0 to 64 kHz range may be produced by varying the ratio of four-bit codes produced by sigma-delta modulator 78. For example, to obtain a sampling frequency between 56 kHz and 64 kHz, the appropriate ratio of +3 and +4 codes would be output by sigma-delta modulator 78 as a function of twenty-bit number 82. One skilled in the art will also appreciate that any sample rate within the working range of the system can be produced through the appropriate combination of four-bit codes. Although a four-bit sigma-delta modulator has been illustrated, the invention is not so limited. For example, a sigma-delta modulator that outputs fewer bits can be used if the modulator is clocked at a faster rate. In the same manner, a sigma-delta modulator that outputs a larger number of bits can be used and the modulator can then be clocked at a lower rate. One skilled in the art will appreciate the the number of bits used and the clock rate used are a function of the desired noise shaping and signal to noise ratio, and may be traded-off depending upon the requirements of a particular application.

One skilled in the art will appreciate that, in the circuit of FIG. 4, both the magnitude and the temporal spacing of the digital samples is sigma-delta encoded by sigma-delta modulator 66 and sigma-delta modulator 78, respectively.

One of the advantages of sigma-delta modulation of the time base is that the jitter or time variation produced on the sampling time (or sampling interval) due to the fact that digital filter 62 or decimator 21 (under control of sigma-delta modulator 20 or 78) respectively produces output samples at time intervals that may not correspond exactly to the specified sampling frequency (3.072 MHz) is varied by the sigma-delta modulator so that any errors that result from the noise or jit