Downsampling Results
Your computed summary appears here above the form after submission.
| Block | Source Index Range | Source X Range | Samples Used | Downsampled Value |
|---|
Calculator Input
Enter a numeric sequence, choose a target size, then apply a downsampling rule.
Example Data Table
This sample uses 12 original points reduced to 6 points with the mean method.
| Block | Original Values | Operation | Downsampled Result |
|---|---|---|---|
| 1 | 4, 7 | (4 + 7) / 2 | 5.5 |
| 2 | 9, 12 | (9 + 12) / 2 | 10.5 |
| 3 | 11, 8 | (11 + 8) / 2 | 9.5 |
| 4 | 6, 5 | (6 + 5) / 2 | 5.5 |
| 5 | 9, 13 | (9 + 13) / 2 | 11.0 |
| 6 | 15, 10 | (15 + 10) / 2 | 12.5 |
Formula Used
For an original sequence with N samples and a requested reduced sequence with M samples, the tool partitions the series into M blocks.
- Compression ratio: R = N / M
- Estimated target interval: Δx_target = Δx_original × N / M
- Block start: s_j = floor(jN / M)
- Block end: e_j = floor((j + 1)N / M) - 1
Each block produces one output value based on the selected rule:
- Mean: y_j = (1 / n_j) Σ x_i
- Median: middle ordered value of the block
- Minimum / Maximum: smallest or largest block value
- Sum: y_j = Σ x_i
- RMS: y_j = sqrt((1 / n_j) Σ x_i²)
- First / Last / Decimation: keep a representative original sample from each block
This grouped formulation handles sequences that do not divide evenly, so every original value contributes to one reduced block.
How to Use This Calculator
- Paste a sequence of numeric values into the input box.
- Enter the number of samples you want after downsampling.
- Select the rule that best matches your goal, such as smoothing, preserving peaks, or keeping totals.
- Set the original interval and starting x value if you want labeled ranges.
- Choose the output precision.
- Press Calculate Downsampling to show the summary above the form.
- Use the CSV or PDF buttons to export the computed table and summary.
Frequently Asked Questions
1. What does downsampling do?
Downsampling reduces the number of samples in a sequence while trying to preserve the important shape, trend, or block behavior of the original data.
2. Which method should I choose?
Use mean or median for smoothing, min or max for extremes, sum for totals, RMS for energy-like signals, and first, last, or decimation when you want direct representatives.
3. What happens when the series length is not divisible evenly?
The tool builds blocks from proportional boundaries. Some blocks may contain one more value than others, but every original sample is still assigned once.
4. Is this suitable for signal processing work?
It is useful for quick mathematical inspection and grouped reduction. For high-fidelity signal processing, dedicated filtering before decimation is usually safer.
5. What is the compression ratio?
The compression ratio compares original sample count to reduced sample count. A ratio of 4 means four original values become one downsampled value.
6. Why does RMS differ from mean?
RMS squares values before averaging, then takes the square root. That gives larger magnitudes more influence than the ordinary mean.
7. Can I export the reduced sequence?
Yes. After calculation, you can download a CSV file for spreadsheets or a PDF file for reports, reviews, or documentation.
8. Does the x interval affect the computed y values?
No. It affects labeling and the estimated target interval. The reduced values themselves come from the numeric sequence and method you choose.