This invention relates generally to digital systems with fractional structures, and more particularly, to systems providing digital delays, especially fractional digital delays.
Digital delay lines are used in electronic systems to compensate for delays in other portions of the systems. A digital delay line ensures that an output signal is delayed by an amount or increment thereof, such as a predetermined time period, relative to an input signal. Thus, an input signal is delayed a certain amount of time (e.g., n time units) by a delay device such that a time delay is introduced between the input to the delay device and the output of the delay device. The delay device may include one or more taps for sampling the digital signal and having different outputs providing different incremental delays. The delay devices may be, for example, a sequential logic element used in digital logic and digital signal processing where the output signal is the same as the input signal at a delayed time.
One application for digital delay lines is in systems having both digital and analog circuitry, such as communication systems, and in particular wireless communication systems (e.g., cellular communication system). In these systems, the digital delay line attempts to compensate for analog delay introduced by the analog circuitry, for example, the analog delay introduced by the analog components, such as filters, capacitors, inductors, etc. If the digital circuitry does not properly compensate for the analog delay problems can arise. For example, the communication system may not be able to meet certain spectral requirements and/or other processes within the system may not be able to function properly because those processes require an accurate measure of the incoming analog signal. As a result, some audio may be distorted or missed entirely.
Known systems for providing delay lines perform an integral delay process that requires multipliers and adders. These systems require complex calculations and processing that can add latency to the overall system and the need for complex controls. Additionally, more power is required to operate these components and more space is required to house these components.
An alternative to providing a digital delay line is to sample the incoming audio signal at a high rate in order to properly process the signal. It is often not easy to sample at these high rates and results in increased power consumption and the need for more components to provide this high rate of sampling, which also results in the need for a larger case for the overall unit. Further, at higher frequency transmissions, for example, 4 GHz, sampling at the required rates is not even possible.
In one embodiment, a digital delay architecture is provided that includes at least one shifter, at least one adder connected to the at least one shifter and a plurality of registers storing at least an output of the at least one adder and an original sampled signal. The plurality of registers are selectable to define a fractional delay value.
In another embodiment, a digital delay architecture is provided that includes an integer delay line having a plurality of integer taps to define an integer delay and a fractional delay line configured to perform linear interpolation to define a fractional delay.
In yet another embodiment, a method for providing a digital delay includes generating an integer delay using a plurality of integer taps. The method further includes generating a fractional delay using at least one shifter.
For simplicity and ease of explanation, the invention will be described herein in connection with various embodiments thereof. Those skilled in the art will recognize, however, that the features and advantages of the various embodiments may be implemented in a variety of configurations. It is to be understood, therefore, that the embodiments described herein are presented by way of illustration, not of limitation.
Various embodiments of the present invention provide a delay for digital systems, especially digital systems with fractional structures. In general, the various embodiments provide fractional delays in incremental powers (e.g., powers of two) and/or fractional decimal delays. Although the various embodiments are described in connection with a particular application, for example, a wireless communication system for communicating audio, the various embodiments may be implemented in any system where digital delay lines are desired or needed and wherein different types of content are communicated.
In operation, the same received signal may be communicated through two paths in the communication unit 20 such that the two signals travel through different circuitry. After the signals pass through the two paths, for example, processed in different components, the processed signals may arrive at an output in the processor 24 shifted in time with respect to each other. This shift in time may be due to different factors, for example, signals require more time to travel through analog paths versus digital paths. These offset signals are aligned in time using the delay generator 26.
The delay generator 26 is shown in more detail in
The delay generator 26 is connected to a controller 36 that controls the operation of the delay generator 26. The controller 36 is connected to a delay estimator 38 that provides control signals to the controller that identifies the amount of delay needed. In operation, a path delay is estimated by the delay estimator 38 in any known manner, and as described in more detail below. The path delay may be estimated, for example, using a process such as synchronization that determines the path delay based on the alignment of amplitude and phase. Such a synchronization process useful for determining path delay is described in commonly assigned co-pending U.S. Patent Application entitled “Apparatus, System, and Method for Amplitude-Phase Synchronization in Polar Transmitter” having Ser. No. 11/396,122, filed Mar. 30, 2006, the entire disclosure of which is hereby incorporated by reference in its entirety. Other processes for estimating the path delay also may be provided, for example, by measurement.
For example, the amplitude and/or phase delay (or a correlation thereof) of a signal of interest, such as a received audio signal or an audio signal to be transmitted, is estimated. The determined estimated delay is then communicated to the controller 36 for use in controlling the delay generator 26 to generate the necessary delay. The amount of delay needed may be expressed, for example, as a time period, a number of clock cycles (and/or a fraction thereof), etc. The delay generator 26 then generates the delay that is introduced into the system or circuit where needed. For example, the estimated delay may be used in an amplitude or phase path to correctly align the two signals depending on which of the signals requires correction (e.g., correct the alignment of the signals). The delay may be provided in different portions of the system or circuit, for example, as digital audio delay lines, etc.
More particularly, for a continuous time system with an arbitrary delay, consider a delay element, which is a linear system with a purpose to delay an incoming continuous-time signal xc(t) by τ (in seconds). The output signal yc(t) of this system can be expressed as:
y
c(t)=xc(t−τ) (1)
where the subscript ‘c’ refers to ‘continuous-time’. The Fourier transform Xc(Ω) of a continuous-time signal xc(t) is then defined as:
where Q=2πf is the angular frequency in radians. The Fourier transform Yc(Ω) of the delayed signal yc(t) can be expressed in terms of Xc(Ω) as:
The transfer function Hd(Ω) of the delay element then can be expressed by means of Fourier transforms Xc(Ω) and Yc(Ω) as follows:
The term e−jΩτ corresponds to the Fourier transform of the delay of τ.
For a discrete time delay system, the Fourier transform Xc(Ω) is non-zero only on a finite interval around ω=0, and the continuous-time signal xc(t) is said to be band limited. The time signal may then be expressed by its samples x(nT), where nεZ is the sample index and T is the sample interval (i.e., the inverse of the sampling rate). In the discrete time version, the delay operation for a sampled band limited signal y(nT) can be expressed as:
y(nT)=x(nT−D) (5)
where D=τ/T is the desired delay as multiples of the unit delay. It should be noted that τ/T is generally irrational since T is usually not an integral multiple of sampling interval T. Equation 5 is meaningful only for integral values of D. The samples of the output sequence y(nT) are equal to the delayed samples of the input sequence x(nT) and the delay element may be called a digital delay line. If D were real, then the delay operation would not be this simple because the output value would be somewhere between the known samples of x(nT). The sample values of y(nT) would then have to be obtained by way of interpolation from the sequence x(nT). The spectrum of a discrete-time signal can be expressed by means of the discrete-time Fourier transform (DTFT). In this integral transform, the time variable is discretized, but the frequency variable is continuous. The DTFT of signal x(nT) is defined as:
where ω=2πfT is the normalized angular frequency. The DTFT of the output signal y(nT) can be expressed as:
The transfer function of an ideal discrete-time delay element can be expressed as:
Replacing the continuous Fourier transform operator, which is representative of the angular frequency, with the discrete time z-transform operator representative of the circular frequency due to discretization, Equation 8 now becomes:
where D□R+ is the length of the delay in samples. The delay D can be expressed as:
D=D
int
+D
frac (10)
where Dint is the integer delay and Dfrac is the fraction whose range is between
0≦Dfrac<1.
In order to produce a fractional delay in the discrete time system the signal is interpolated. Interpolation of a discrete time signal is possible because the amplitude of the corresponding continuous time band limited signal changes smoothly between the sampling instants. The value of the fractional delay can in principle be any value between 0 and 1. In order to produce any arbitrary fractional delay for a discrete time signal x(nT), it must be known how to compute the amplitude of the underlying continuous time signal x(t) for all t.
Shannon's sampling theorem states that in order to reconstruct any signal within intervals (−fc, fc) in the Fourier domain the signal needs to be sampled at twice the rate of fc. Using cardinal series, the reconstruction formula for a sampled signal is:
where ωs=2πfs is the sampling angular frequency in radians per second and T=1/fs is the corresponding sampling interval. The sinc function is defined as:
From Equation 11, the ideal band limited interpolator has a continuous time impulse response as follows:
The desired delay D may be obtained by shifting Equation 13 by D and then sampling D at equidistant points. Hence the output y(n) of the ideal discrete time fractional delay element is computed as:
for nεZ and DεR. Thus, in order to produce a fractional delay reconstruction of the discrete time signal and shifted re-sampling of the resulting continuous time signal as represented in Equation 14 is performed.
The desired delay D may be generated using the delay generator 26 by generating a fractional digital delay and an integer digital delay (also referred to as a real digital delay). The fractional delay line 30 may be implemented to generate different incremental fractional delays, the resolution of which is based on the number of taps 34 provided. The fractional delay is generated without the use of digital multipliers. In general, the fractional delay line 30 is formed from a digital architecture, for example in an ASIC, wherein different resolutions may be provided as defined by ½N, where N is the number of taps of the fractional delay structure. In particular, the fractional delay line 30 may be implemented using a two tap structure 50 as shown in
Referring to
In operation, the input signals are subtracted by the subtractor and then shifted by one by the shifter 54 (e.g., a one binary bit shift). Thereafter the output of the shifter 54 is added to the signal to be delayed and stored in the second register 60 with the original signal stored in the first register 58. The registers 58 and 60, and generally as described herein, are storage elements configured to hold or store signal value or data, which in this embodiment, operate as delay elements. Thereafter, different combinations of the register outputs may be selected such that Dfrac can be two different values, namely 0 and 0.5.
Referring to
Referring to
Thus, for the two tap structure 50, a fractional resolution of 1/2 is provided. For the four tap structure 70, a fractional resolution of ¼ is provided. For the eight tap structure 90, a fractional resolution of ⅛ is provided. Additional embodiments are contemplated with different numbers of taps to provide different levels of resolution such that for an N tap structure the fractional resolution is 1/N where N is a power of two.
Further, the fractional delay line 30 may be provided with higher order taps with the order for this fractional delay line being a power of 2. Accordingly, for an N=2p tap structure with N registers, p shifters would be required and p*2p-1 adders would be required, with p being a positive integer value.
In another embodiment as shown in
In operation, the signals x(n) and x(n−1) are received at the input of the subtractor 52, the output of which is shifted by the all the shifters 120-134 (such that a fractional precision of eight bits is provided) that are then switched depending on the bits in the registers 136-150, namely Dfrac registers [b7b6b5b4b3b2b1b0]. If the corresponding bit is a ‘1’ then the output of the shifter is selected and if the output is a ‘0’ then the value=0 (GND) is selected and fed to the adders 56. This operation is performed by all the switches and after traversing through the different adders in the path the final output is a fractional delayed by Dfrac, namely x(n−Dfrac).
Various embodiments provide a delay that is defined by a fractional component generated by the fractional delay line 30 as described above and an integer delay component generated by an integer delay line 32 as described in more detail below. Thus, a combination of integer delays plus fractional delays is provided. As shown in
In operation, the value of the taps 34 is determined by the duration of the delay required and the clock rate at which the delay line operates. The Dint signal input to the first multiplexer 162 selects the integer delay tap (e.g., tap value) through the first multiplexer 162 with the first multiplexer 162 connected to the x(n) input of the fractional delay line 30 providing that tap value to the x(n) input. The Dint+1 signal is input to the second multiplexer 164 to select the integer delay tap through the second multiplexer 164 with the second multiplexer 162 connected to the x(n−1) input of the fractional delay line 30 providing the tap value to the x(n−1) input. The fractional part of the value (e.g., a fractional value for which the delay needs to be provided) is registered as Dfrac that takes only fractional values that are a power of two as described above. The Dfrac value is used by the selector 64 (shown in
Thus, the signal s(kT) to be delayed by an amount Dint+Dfrac is fed to the integer delay line 32 shown in
The integer delay line 32 delays the input s(kT) by an amount Dint and, thus, the input x(n) and x(n−1) are defined as follows:
x(n)=s(kT−Dint (15)
x(n−1)=s(kT−Dint−1) (16)
The output of the fractional delay line 30, which is also the final output of the real digital delay structure, is the signal s(kT) is delayed by a real value amount Dint+Dfrac, thus generating a signal equal to s(kT−Dint−Dfrac).
In the various embodiments, and referring, for example, to
It should be noted that for a delay, for example, the delay of 2.25, the sequence for the delay may vary from time to time. For example, and using the delay of 2.25, if the sampling rate is 52 MHz (about 19.23 nanoseconds (ns)), then a delay of 2.25 translates to a 43.26 ns delay. In this delay of 43.26 ns, 38.46 ns is translated (and corresponds) to two integer delays and the remaining 4.80 ns is translated (and corresponds) to a 0.25 fractional delay (which is the fractional delay portion).
Thus, the various embodiments provide a digital delay structure that implements fractional delays without the use of multipliers. This implementation results in reduced power consumption and less space needed to accommodate the structure.
While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the various embodiments of the invention can be practiced with modification within the spirit and scope of the claims.