Generating gradient signal

1. A method of generating a gradient signal, comprising:

obtaining a target amplitude and a target duration associated with a target precision corresponding to the gradient signal;

generating a first actual amplitude by intercepting the target amplitude according to an actual precision of a digital to analog converter (DAC);

generating a second actual amplitude according to the first actual amplitude, wherein a difference between the second actual amplitude and the first actual amplitude is 1;

determining a first actual duration of outputting the first actual amplitude and a second actual duration of outputting the second actual amplitude according to the target amplitude, the target duration, the first actual amplitude and the second actual amplitude; and

controlling the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration.

2. The method of claim 1 , wherein determining the first actual duration of outputting the first actual amplitude and the second actual duration of outputting the second actual amplitude according to the target amplitude, the target duration, the first actual amplitude and the second actual amplitude comprises:

generating a first equivalent relationship to indicate that a target area is equal to a product of an area sum and a n-th power of 2, wherein:

the target area is a product of the target amplitude and the target duration;

the area sum is a sum of a first area and a second area;

the first area is a product of the first actual amplitude and the first actual duration;

the second area is a product of the second actual amplitude and the second actual duration;

n is a difference between the number of valid bits of the target precision and the number of valid bits of the actual precision;

generating a second equivalent relationship to indicate that the target duration is equal to a sum of the first actual duration and the second actual duration;

determining the first actual duration and the second actual duration according to the first equivalent relationship and the second equivalent relationship.

3. The method of claim 1 , wherein controlling the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration comprises:

controlling, in the target duration, the DAC to:

firstly outputting the first actual amplitude in the first actual duration;

subsequently outputting the second actual amplitude in the second actual duration.

4. The method of claim 1 , wherein controlling the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration comprises:

controlling, in the target duration, the DAC to:

firstly outputting the second actual amplitude in the second actual duration;

subsequently outputting the first actual amplitude in the first actual duration.

5. The method of claim 1 , wherein controlling the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration comprises:

controlling, in the target duration, the DAC to alternately output the first actual amplitude and the second actual amplitude, wherein

a sum of durations of outputting the first actual amplitude is equal to the first actual duration,

a sum of durations of outputting the second actual amplitude is equal to the second actual duration.

6. A gradient signal generator, comprising:

a Digital to Analog Converter (DAC),

a processor,

a non-transitory machine-readable storage medium storing machine executable instructions which are executable by the processor to:

obtain a target amplitude and a target duration associated with a target precision corresponding to the gradient signal;

generate a first actual amplitude by intercepting the target amplitude according to an actual precision of the DAC;

generate a second actual amplitude according to the first actual amplitude, wherein a difference between the second actual amplitude and the first actual amplitude is 1;

determine a first actual duration of outputting the first actual amplitude and a second actual duration of outputting the second actual amplitude according to the target amplitude, the target duration, the first actual amplitude and the second actual amplitude; and

control the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration.

7. The generator of claim 6 , wherein the processor is caused by the machine-executable instructions to:

generate a first equivalent relationship to indicate that a target area is equal to a product of an area sum and a n-th power of 2, wherein:

the target area is a product of the target amplitude and the target duration;

the area sum is a sum of a first area and a second area;

the first area is a product of the first actual amplitude and the first actual duration;

the second area is a product of the second actual amplitude and the second actual duration;

n is a difference between the number of valid bits of the target precision and the number of valid bits of the actual precision;

generate a second equivalent relationship to indicate that the target duration is equal to a sum of the first actual duration and the second actual duration;

determine the first actual duration and the second actual duration according to the first equivalent relationship and the second equivalent relationship.

8. The generator of claim 6 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to:

firstly output the first actual amplitude in the first actual duration;

subsequently output the second actual amplitude in the second actual duration.

9. The generator of claim 6 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to:

firstly output the second actual amplitude in the second actual duration;

subsequently output the first actual amplitude in the first actual duration.

10. The generator of claim 6 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to alternately output the first actual amplitude and the second actual amplitude, wherein

a sum of durations of outputting the first actual amplitude is equal to the first actual duration,

a sum of durations of outputting the second actual amplitude is equal to the second actual duration.

11. A magnetic resonance imaging system, comprising a three-dimensional gradient subsystem configured to provide a gradient magnetic field, wherein

the three-dimensional gradient subsystem comprises a gradient waveform generator,

the gradient waveform generator comprises:

a Digital to Analog Converter (DAC),

a processor,

a non-transitory machine-readable storage medium storing machine executable instructions which are executable by the processor to:

obtain a target amplitude and a target duration associated with a target precision corresponding to the gradient signal;

generate a first actual amplitude by intercepting the target amplitude according to an actual precision of the DAC;

generate a second actual amplitude according to the first actual amplitude, wherein a difference between the second actual amplitude and the first actual amplitude is 1;

determine a first actual duration of outputting the first actual amplitude and a second actual duration of outputting the second actual amplitude according to the target amplitude, the target duration, the first actual amplitude and the second actual amplitude; and

control the DAC to output the first actual amplitude according to the first actual duration and to output the second actual amplitude according to the second actual duration.

12. The system of claim 11 , wherein the processor is caused by the machine-executable instructions to:

generate a first equivalent relationship to indicate that a target area is equal to product of an area sum and a n-th power of 2, wherein:

the target area is a product of the target amplitude and the target duration;

the area sum is a sum of a first area and a second area;

the first area is a product of the first actual amplitude and the first actual duration;

the second area is a product of the second actual amplitude and the second actual duration;

n is a difference between the number of valid bits of the target precision and the number of valid bits of the actual precision;

generate a second equivalent relationship to indicate that the target duration is equal to a sum of the first actual duration and the second actual duration;

determine the first actual duration and the second actual duration according to the first equivalent relationship and the second equivalent relationship.

13. The system of claim 11 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to:

firstly output the first actual amplitude in the first actual duration;

subsequently output the second actual amplitude in the second actual duration.

14. The system of claim 11 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to:

firstly output the second actual amplitude in the second actual duration;

subsequently output the first actual amplitude in the first actual duration.

15. The system of claim 11 , wherein the processor is caused by the machine-executable instructions to:

control, in the target duration, the DAC to alternately output the first actual amplitude and the second actual amplitude, wherein

a sum of durations of outputting the first actual amplitude is equal to the first actual duration,

a sum of durations of outputting the second actual amplitude is equal to the second actual duration.