Unit conversion mm/sqrt(Hz)/degree to m^2/Hz/rad

[robbie.]

Hello,

I have two datasets containing power spectral density data to be compared. One of these datasets is presented in units mm/sqrt (Hz)/degree, and I would like to do some transformation so that data is comparable with the other set, which has units m^2/Hz/rad.

Any help on how to do this would be massively appreciated, as this kind of thing is not my strong point!

Many thanks,

Robbie

 

[Simon Bridge]

They look like they've each measured something different - they have different dimensions.

The first units look like
$$\left ( \frac{mm^2}{Hz} \right )^{1/2}\text{deg}^{-1}$$

So this is the square-root of the other one scaled for degrees.
I would reverse the per-degree part of the calculation and square it to get the same thing, then bother with converting the units.

 

[robbie.]

Thank you for your reply, however I am struggling to understand what you mean when you say 'reverse' the per degree part?

 

[Simon Bridge]

The numbers had to be calculated somehow that ended up with the units being "per degree" ... whatever they did, do the opposite. eg. if they divided by 360, then multiply by 360.

Put another way:
If there are X (mm²/Hz)^1/2 in one degree ... then how many mm²/Hz are there in 1 degree?

 

[CellCoree]

Hello Robbie,

Unit conversion can often be a tricky task, but it is important in order to compare data accurately. In this case, you will need to convert the units of the first dataset from mm/sqrt(Hz)/degree to m^2/Hz/rad. This can be done using the following steps:

1. Convert mm to m: Since 1 mm = 0.001 m, you will need to multiply the values in the first dataset by 0.001.

2. Convert sqrt(Hz) to Hz: The square root of Hz is the same as Hz raised to the power of 1/2. So, you will need to raise the values in the first dataset to the power of 1/2.

3. Convert degree to radian: Since 180 degrees = pi radians, you will need to multiply the values in the first dataset by pi/180.

After completing these steps, the units of the first dataset will be in m^2/Hz/rad, making it comparable to the second dataset. It is important to note that in scientific notation, the unit for square root is often represented as 1/2. So, the conversion can also be written as m^(1/2)/Hz^(1/2)/rad.

I hope this helps with your data comparison. If you have any further questions, please let me know. Best of luck with your research!

Sincerely,