Calculator Inputs
Example Data Table
| Use Case | Image Size | Family | Operation | Primary Cutoff | Upper Cutoff | Order | Typical Outcome |
|---|---|---|---|---|---|---|---|
| Noise smoothing | 1024 × 1024 | Gaussian | Low-pass | 0.90 cycles/mm | 1.50 cycles/mm | 2 | Softer texture and reduced fine-grain noise. |
| Edge emphasis | 2048 × 2048 | Butterworth | High-pass | 1.20 cycles/mm | 1.80 cycles/mm | 3 | Sharper boundaries with controlled transition steepness. |
| Stripe removal | 1536 × 1024 | Butterworth | Notch reject | 0.80 cycles/mm | 1.40 cycles/mm | 4 | Periodic interference is reduced around selected notches. |
Formula Used
Frequency-plane distance: D(u,v) = √(u² + v²)
Sampling frequency: fx = 1 / Δx and fy = 1 / Δy
Nyquist limits: fx/2 and fy/2
Ideal low-pass: H(D) = 1 for D ≤ D0, otherwise 0
Butterworth low-pass: H(D) = 1 / [1 + (D / D0)^(2n)]
Gaussian low-pass: H(D) = exp[-D² / (2D0²)]
High-pass filters: use the complementary low-pass behavior, so preserved low frequencies become suppressed and higher frequencies are retained.
Band filters: the calculator estimates a ring-shaped kept or rejected region using lower cutoff, upper cutoff, and bandwidth.
Notch filters: the calculator evaluates paired notches at (±u0, v0) with radius r to reject or keep periodic frequency components.
Estimated retained spectrum: this summary uses a weighted average of the transfer function across the plotted radial range.
How to Use This Calculator
- Enter the image width, image height, and pixel pitch values.
- Choose the spatial unit so the frequency labels stay meaningful.
- Select the filter family: ideal, Butterworth, or Gaussian.
- Choose the operation that matches your goal, such as smoothing, edge emphasis, band isolation, or stripe removal.
- Enter the cutoff values, bandwidth, and order. Add notch center and radius for notch designs.
- Press the calculate button to see the summary, checkpoint table, and frequency response graph.
- Use the CSV or PDF buttons to export the computed summary.
Frequently Asked Questions
1) What does this calculator estimate?
It estimates how a chosen Fourier-domain filter behaves across spatial frequencies. It reports cutoff effects, retained spectrum, suppression level, checkpoint gains, and a plotted response slice for quick interpretation.
2) When should I choose an ideal filter?
Choose an ideal filter when you want an abrupt cutoff. It is mathematically simple, but it usually creates stronger ringing because the transition between kept and removed frequencies is very sharp.
3) Why use Butterworth instead of Gaussian?
Butterworth filters let you control transition steepness with the order value. Gaussian filters are smoother and usually produce less ringing, but they do not provide the same sharp adjustable slope.
4) What does cutoff frequency mean here?
Cutoff frequency marks the boundary where the filter starts changing what it keeps or suppresses. Lower cutoffs preserve coarser structures, while higher cutoffs keep more fine detail.
5) Why are two cutoffs useful for band-pass and band-stop?
Two cutoffs define a frequency interval. Band-pass keeps frequencies inside that interval, while band-stop removes them. This helps isolate texture ranges or suppress specific repeating patterns.
6) What does filter order change?
Order mainly affects Butterworth sharpness. A higher order creates a steeper rolloff near the cutoff, which improves selectivity but can increase ringing risk and sensitivity to parameter choices.
7) What are notch filters used for?
Notch filters target narrow frequency locations, often used to reduce periodic noise such as stripes, sensor interference, or repeating scan artifacts. They are especially useful when the unwanted pattern is localized.
8) Does a higher retained spectrum always mean a better image?
No. Better results depend on the task. Heavy smoothing can improve denoising but blur edges, while stronger high-pass settings can sharpen edges yet also amplify noise and artifacts.