CN103577152A - Method for enlarging SFDR (spurious free dynamic range) of signal after data truncation - Google Patents

Abstract

The invention provides a method for enlarging an SFDR (spurious free dynamic range) of a signal after data truncation. A uniformly distributed random integer signal sequence in a certain amplitude range is generated through design, the bit width of the random integer signal sequence is identical with the truncated bit width, the random integer signal sequence is stacked on a signal before truncation, then bit width truncation is performed, and a random signal after truncation is obtained, so that the harmonic amplitude of the truncation error is decayed rapidly, harmonic distortion caused by direct truncation is eliminated, and the dynamic range of the random signal after truncation is enlarged.

Description

A kind of method that improves signal Spurious Free Dynamic Range after data cut position

Technical field

The invention belongs to digital signal processing technique field, more specifically say, relate to a kind of method that improves signal Spurious Free Dynamic Range after data cut position.

Background technology

At present, the main devices that realizes digital signal processing is FPGA and DSP.Digital processing device all can be subject to the impact of " finite word length effect ", and each value of burst is all that form with limited bit wide exists.In general, the various computings of carrying out in FPGA all complete based on integer number, therefore, in FPGA internal arithmetic process, computing each time all may bring the increase of data bit width, cause the final operation result bit wide needed bit wide that surpasss the expectation, at this moment need final operation result to carry out cut position processing; Or when rear class processing bit wide is lower, also need the high-bit width operation result cut position of prime to process.The maximum bit wide that for example inner Fast Fourier Transform (FFT) (FFT) IP of the most of fpga chip core of ALTERA company can support is 24, if input signal is after a plurality of operations such as quantification, mixing, filtering and windowing, final operation result bit wide likely can be greater than 24.At this time, need to clip unnecessary figure place to meet the requirement of 24.

In the prior art, the common cut position way of digital signal processing is directly to cut out minimum a few positions, the bit wide requirement of processing to meet rear class, this direct cut position to long numeric data is processed, realization is the transfer process from high quantization precision to low quantified precision by data, in transfer process, minimizing due to data quantization step, the information of describing signal detail between adjacent two sampling points also reduces thereupon, the continuous change information that causes a plurality of sampled points of high quantization precision signal to represent becomes one-level and does not have vicissitudinous ladder, cause the low quantified precision signal obtaining to occur obvious harmonic distortion, reduce the Spurious Free Dynamic Range (SFDR) of the rear signal of conversion.

Suppose that x (n) is the final signal obtaining after a series of computings, effectively bit wide is A, and the signal obtaining after data cut position is y (n), and number of significant digit is B.If z (n) represents the error signal of clipping, bit wide is A-B, has following relation to set up:

x(n)＝y(n)*2 ^A-B+z(n) （1）

If the discrete Fourier transformation (DFT) of x (n), y (n) and z (n) is respectively X (e ^{j ω}), Y (e ^{j ω}) and Z (e ^{j ω}), discrete Fourier transformation is asked in (1) formula equal sign both sides:

$\begin{array}{c}X\left(e^{\mathrm{j\ω}}\right)=\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}x\left(n\right)e^{-\mathrm{j\ωn}}\\ =\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}[y\left(n\right)*2^{A-B}+z\left(n\right)]e^{-\mathrm{j\ωn}}\\ =\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}y\left(n\right)*2^{A-B}{e}^{-\mathrm{j\ωn}}+\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}z\left(n\right)e^{-\mathrm{j\ωn}}\\ =2^{A-B}\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}y\left(n\right)e^{-\mathrm{j\ωm}}+\underset{n=0}{\overset{\∞}{\mathrm{\Σ}}}z\left(n\right)e^{-\mathrm{j\ωn}}\end{array}---\left(2\right)$

That is: X (e ^{j ω})=2 ^a-By(e ^{j ω})+Z (e ^{j ω}) (3)

From formula (3), can find out, in the situation that the relevant frequency spectrum parameter of x (n) is certain, the Frequency spectrum quality of the signal y (n) that cut position obtains is subject to the impact of cut position error z (n).

What z (n) represented is the A-B bit error signal of clipping, z (n)=x (n) (mod2 ^a-B), mod is congruence, represents to get x (n) divided by 2 ^a-Bthe remainder obtaining.

At x (n) ∈ [0,2 ^a-1], in scope, cut position error signal z (n) is with N(N=2 ^a-B) be the discrete sawtooth wave function in cycle, and when x (n) ∈ [0, N-1], z (n)=n.Can obtain thus the Fourier expansion formula of N point z (n):

$z\left(n\right)=\underset{k=<N>}{\mathrm{\&Sigma;}}{a}_k{e}^{\mathrm{jk}{\mathrm{\&omega;}}_{0}n}=\underset{k=<N>}{\mathrm{\&Sigma;}}{a}_k{e}^{\mathrm{jk}(2\mathrm{\&pi;}/N)n}---\left(4\right)$

Fourier series coefficient a wherein _kvalue be:

$\begin{array}{c}{a}_k=\frac{1}{N}\underset{k=<N>}{\mathrm{\&Sigma;}}z\left(n\right)e^{-\mathrm{jk}{\mathrm{\&omega;}}_{0}n}\\ =\frac{1}{N}\underset{k=<N>}{\mathrm{\&Sigma;}}z\left(n\right)e^{-\mathrm{jk}(2\mathrm{\&pi;}/N)n}\\ =\frac{\cos (2\mathrm{\&pi;k}/N)-1+j\sin (2\mathrm{\&pi;k}/N)}{2[1-\cos (2\mathrm{\&pi;k}/N)]}\\ =\frac{{\mathrm{je}}^{\mathrm{j\&pi;k}/N}}{2\sin (\mathrm{\&pi;k}/N)}\end{array}---\left(5\right)$

By formula (6), can obtain the expression formula of periodic signal z (n) Fourier transform in one-period is:

$Z\left(e^{\mathrm{j\&omega;}}\right)=\mathrm{j\&pi;}\underset{k=<N>}{\mathrm{\&Sigma;}}\frac{e^{\mathrm{j\&pi;k}/N}}{\sin (\mathrm{\&pi;k}/N)}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})---\left(6\right)$

K value hour, amplitude versus frequency characte function representation as shown in the formula:

$\left|Z\left(e^{\mathrm{j\&omega;}}\right)\right|=\underset{k}{\mathrm{\&Sigma;}}\frac{N}{k}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})---\left(7\right)$

From formula (7), can find out, harmonic amplitude distributes and has approximate inversely proportional relation with k, decays slower.Cut position error has been introduced the harmonic wave burr with certain amplitude, must cause signal Spurious Free Dynamic Range to decline.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of method that improves signal Spurious Free Dynamic Range after data cut position is provided, eliminate the harmonic distortion that direct cut position causes, improve the dynamic range of signal after cut position.

For achieving the above object, the present invention is a kind of improves the method for signal Spurious Free Dynamic Range after data cut position, it is characterized in that, comprises the following steps:

(1), by random signal generation module, generate random integers burst d, d is uniformly distributed [0, N-1] upper obedience, wherein, and N=2 ^a-B, A be prime module produce by the bit wide of intercept signal x (n), B is signal z (n+d) bit wide after cut position, and A > B, the bit wide of random integers burst d is consistent with the bit wide cutting out;

(2), being added by intercept signal x (n) and random integers burst d that prime module is produced, then cut out minimum A-B position, obtain high B position signal z (n+d), complete cut position operation;

The distribution law function of random integers burst d is p (m), fourier transform p (the e of p (m) ^{j ω}) be:

$\begin{array}{c}P\left(e^{\mathrm{j\&omega;}}\right)=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}p\left(m\right)e^{-\mathrm{j\&omega;m}}\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\frac{1}{N}\&CenterDot;e^{-\mathrm{j\&omega;m}}\\ =\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\end{array}$

If new cut position error signal be z ' (n), z ' (n) can be expressed as:

$\begin{array}{c}{z}^{\&prime;}\left(n\right)=E\left[z(n+d)\right]\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}z(n+m)p\left(m\right)\end{array}$

Wherein, z (n+d) refers to the signal that cut position obtains after cut position front signal x (n) adds random integers burst d;

Z ' (n) is the cross correlation function of signal z (n) and p (m), according to the relation between cross correlation function and convolution function, can obtain z ' spectrum expression formula (n) and is:

Z′(e ^jω)＝Z(e ^-jω)P(e ^jω)

Z ' amplitude versus frequency characte (n) is:

$\begin{array}{c}\left|Z^{\&prime;}\left(e^{\mathrm{j\&omega;}}\right)\right|=\left|Z\left(e^{-\mathrm{j\&omega;}}\right)\right|\left|P\left(e^{\mathrm{j\&omega;}}\right)\right|\\ =\underset{k}{\mathrm{\&Sigma;}}\frac{N}{k}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\&CenterDot;\left|\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\right|\\ =\left|\underset{k}{\mathrm{\&Sigma;}}\frac{1-e^{-\mathrm{j\&omega;N}}}{k(1-e^{-\mathrm{j\&omega;}})}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\right|\\ =0\end{array}.$

Goal of the invention of the present invention is achieved in that

The present invention is a kind of improves the method for signal Spurious Free Dynamic Range after data cut position, what by design, produce certain amplitude scope is uniformly distributed random integers burst, and the bit wide of random integers burst is consistent with the bit wide cutting out, on the signal that random integers burst is added to before cut position, and then carry out bit wide and block, the harmonic amplitude of cut position error is decayed fast, thereby eliminate the harmonic distortion that direct cut position causes, improve the dynamic range of signal after cut position.

Meanwhile, the present invention improves the method for signal Spurious Free Dynamic Range after data cut position and also has following beneficial effect:

(1), the present invention can make the harmonic amplitude of cut position error decay fast, thereby eliminate the harmonic distortion that direct cut position causes, improve the dynamic range of signal after cut position;

(2), the present invention has simple feature, especially in engineering, for digital signal processing, fine to signal Spurious Free Dynamic Range effect of optimization;

(3), the random integers burst bit wide that adopts in the present invention is consistent with the bit wide cutting out, and can not raise because amplitude is excessive like this end of low precision signal after cut position and make an uproar, and also can not change because amplitude is too small the ladder of low precision signal after cut position.

Accompanying drawing explanation

Fig. 1 is a kind of theory diagram of method that the present invention improves signal Spurious Free Dynamic Range after data cut position;

Fig. 2 adopts the signal spectrum before the present invention;

Fig. 3 adopts the signal spectrum after the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described, so that those skilled in the art understands the present invention better.Requiring particular attention is that, in the following description, when perhaps the detailed description of known function and design can desalinate main contents of the present invention, these are described in here and will be left in the basket.

Embodiment

Fig. 1 is a kind of theory diagram of method that the present invention improves signal Spurious Free Dynamic Range after data cut position.In the present embodiment, as shown in Figure 1, random signal generation module is designed to example with FPGA, and in FPGA, the generation of equally distributed random integers burst is by means of the read only memory ROM of matlab instrument and the realization of FPGA internal storage resources, and concrete operation step comprises:

(1), in matlab, to utilize function unidrnd (N, L, 1) to produce length be L at [0, N-1] the upper equally distributed random integers burst d of obedience, wherein, N=2 ^a-Ba be prime module produce by the bit wide of intercept signal x (n), B is signal z (n+d) bit wide after intercepting, and A > B, the bit wide of random integers burst d is consistent with the bit wide cutting out, and generates .mif file, at FPGA, call ROM core and load .mif file, generate new ROM core, new ROM core bit wide is A-B, and the degree of depth is L;

(2), will be added by the random integers burst d of intercept signal x (n) and ROM storage, then cut out minimum A-B position, obtain high B position signal z (n+d), complete cut position operation;

The distribution law function of random integers burst d is p (m),

fourier transform p (the e of p (m) ^{j ω}) be:

$\begin{array}{c}P\left(e^{\mathrm{j\&omega;}}\right)=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}p\left(m\right)e^{-\mathrm{j\&omega;m}}\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\frac{1}{N}\&CenterDot;e^{-\mathrm{j\&omega;m}}\\ =\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\end{array}$

If new cut position error signal be z ' (n), z ' (n) can be expressed as:

$\begin{array}{c}{z}^{\&prime;}\left(n\right)=E\left[z(n+d)\right]\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}z(n+m)p\left(m\right)\end{array}$

Wherein, z (n+d) refers to the signal that cut position obtains after cut position front signal x (n) adds random integers burst d;

Z ' (n) is the cross correlation function of signal z (n) and p (m), according to the relation between cross correlation function and convolution function, can obtain z ' spectrum expression formula (n) and is:

Z′(e ^jω)＝Z(e ^-jω)P(e ^jω)

Z ' amplitude versus frequency characte (n) is:

$\begin{array}{c}\left|Z^{\&prime;}\left(e^{\mathrm{j\&omega;}}\right)\right|=\left|Z\left(e^{-\mathrm{j\&omega;}}\right)\right|\left|P\left(e^{\mathrm{j\&omega;}}\right)\right|\\ =\underset{k}{\mathrm{\&Sigma;}}\frac{N}{k}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\&CenterDot;\left|\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\right|\\ =\left|\underset{k}{\mathrm{\&Sigma;}}\frac{1-e^{-\mathrm{j\&omega;N}}}{k(1-e^{-\mathrm{j\&omega;}})}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\right|\\ =0\end{array}.$

Fig. 2 adopts the signal spectrum before the present invention.

Fig. 3 adopts the signal spectrum after the present invention.

As shown in Figure 2, it is the signal spectrum of not processing through the present invention, on whole frequency spectrum, can observe harmonic component and not obtain fine inhibition, the harmonic wave burr with certain amplitude, the signal of processing by the present invention as shown in Figure 3, the harmonic component of this frequency spectrum obtains fine inhibition, improves signal Spurious Free Dynamic Range successful.

Although above the illustrative embodiment of the present invention is described; so that those skilled in the art understand the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various variations appended claim limit and definite the spirit and scope of the present invention in, these variations are apparent, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (1)

1. a method that improves signal Spurious Free Dynamic Range after data cut position, is characterized in that, comprises the following steps:

(1), by random signal generation module, generate random integers burst d, d is uniformly distributed [0, N-1] upper obedience, wherein, and N=2 ^a-B, A be prime module produce by the bit wide of intercept signal x (n), B is signal z (n+d) bit wide after cut position, and A > B, the bit wide of Random number sequence d is consistent with the bit wide cutting out;

(2), being added by intercept signal x (n) and random integers burst d that prime module is produced, then cut out minimum A-B position, obtain high B position signal z (n+d), complete cut position operation;

The distribution law function of random integers burst d is p (m),

fourier transform p (the e of p (m) ^{j ω}) be:

$\begin{array}{c}P\left(e^{\mathrm{j\&omega;}}\right)=\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}p\left(m\right)e^{-\mathrm{j\&omega;m}}\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}\frac{1}{N}\&CenterDot;e^{-\mathrm{j\&omega;m}}\\ =\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\end{array}$

If new cut position error signal be z ' (n), z ' (n) can be expressed as:

$\begin{array}{c}{z}^{\&prime;}\left(n\right)=E\left[z(n+d)\right]\\ =\underset{m=0}{\overset{N-1}{\mathrm{\&Sigma;}}}z(n+m)p\left(m\right)\end{array}$

Wherein, z (n+d) refers to the signal that cut position obtains after cut position front signal x (n) adds random integers burst d;

Z ' (n) is the cross correlation function of signal z (n) and p (m), according to the relation between cross correlation function and convolution function, can obtain z ' spectrum expression formula (n) and is:

Z′(e ^jω)＝Z(e ^-jω)P(e ^jω)

Z ' amplitude versus frequency characte (n) is:

$\begin{array}{c}\left|Z^{\&prime;}\left(e^{\mathrm{j\&omega;}}\right)\right|=\left|Z\left(e^{-\mathrm{j\&omega;}}\right)\right|\left|P\left(e^{\mathrm{j\&omega;}}\right)\right|\\ =\underset{k}{\mathrm{\&Sigma;}}\frac{N}{k}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\&CenterDot;\left|\frac{1-e^{-\mathrm{j\&omega;N}}}{N(1-e^{-\mathrm{j\&omega;}})}\right|\\ =\left|\underset{k}{\mathrm{\&Sigma;}}\frac{1-e^{-\mathrm{j\&omega;N}}}{k(1-e^{-\mathrm{j\&omega;}})}\mathrm{\&delta;}(\mathrm{\&omega;}-\frac{2\mathrm{\&pi;k}}{N})\right|\\ =0\end{array}.$

Images