To calculate the Root Mean Square Average (RMA), also known as the Root Mean Square (RMS) for the provided data, we can follow these steps:

Steps for calculating RMA (RMS):

1. Window Size: The RMA is calculated over a moving window size of 3, which means that for each point, we take the last 3 values, compute their square, and then take the square root of the mean of those squares.

2. Formula for RMA: $RMA(t) = \sqrt{\frac{1}{N} \sum_{i=1}^{N} (x(t-i))^2}$ Where:

   • $N = 3$ (since the window size is 3).
   • $x(t)$ is the data point at time $t$.
   • For each value of $t$, compute the RMS of the last 3 values: $x(t-2), x(t-1), x(t)$.

Applying this to your data (Window size = 3):

The given data values are:

• 236.16, 237.16, 238.16, 239.16, 240.16, 241.16, 242.16, 243.16, 244.16, 245.16, 246.16

We will compute the RMA at each timestamp from the 3rd value onward (because for the first two, there aren't enough previous values to form a window of size 3).

Let's calculate this for the first few values.

Step-by-step for RMA:

1. For timestamp 3 (value = 238.16):

   • Values in the window: [236.16, 237.16, 238.16] $RMA(3) = \sqrt{\frac{1}{3} \left( 236.16^2 + 237.16^2 + 238.16^2 \right)}$ Let's calculate this value.

2. For timestamp 4 (value = 239.16):

   • Values in the window: [237.16, 238.16, 239.16] $RMA(4) = \sqrt{\frac{1}{3} \left( 237.16^2 + 238.16^2 + 239.16^2 \right)}$ Let's calculate this value.

3. For timestamp 5 (value = 240.16):

   • Values in the window: [238.16, 239.16, 240.16] $RMA(5) = \sqrt{\frac{1}{3} \left( 238.16^2 + 239.16^2 + 240.16^2 \right)}$ And so on, for the rest.

I'll now compute this. numpy as np

Provided data values

data = [236.16, 237.16, 238.16, 239.16, 240.16, 241.16, 242.16, 243.16, 244.16, 245.16, 246.16]

Function to calculate RMA (Root Mean Average) for a given data set with window size of 3

def calculate_rma(data, window_size=3): rma_values = [] for i in range(window_size - 1, len(data)): window = data[i - (window_size - 1): i + 1] rma = np.sqrt(np.mean(np.square(window))) rma_values.append(rma) return rma_values

Calculate RMA values

rma_values = calculate_rma(data)

Results for RMA starting from timestamp 3

rma_valuesThe calculated Root Mean Square Average (RMA) values (voltage in line 1, VLN) with a window size of 3 are:

• For timestamp 3: 237.16
• For timestamp 4: 238.16
• For timestamp 5: 239.16
• For timestamp 6: 240.16
• For timestamp 7: 241.16
• For timestamp 8: 242.16
• For timestamp 9: 243.16
• For timestamp 10: 244.16
• For timestamp 11: 245.16

These RMA values represent the voltage at each timestamp considering a 3-point window average. The values gradually increase because the input data increases in a linear pattern.

Would you like more details on how the calculation works or need any additional analysis? Here's a list of related questions:

1. How would changing the window size affect the RMA calculation?
2. What is the difference between RMA and other moving averages like SMA (Simple Moving Average)?
3. How can I apply this RMA formula to larger datasets in a programming environment?
4. How is RMA used in signal processing or electrical engineering?
5. Can RMA be used for analyzing noisy data, and how does it help?

Tip: When using RMA or similar calculations, always consider the size of your data and the impact of the window size on smoothing and trends. Larger windows smooth the data more but may lose finer details.