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Usage Guide

Interface Layout

┌──────────────────────────────────────────────────────────────────────┐
│  📡  Fourier Studio     [ Mixer ]  [ Emphasizer ]                  [◐ DARK]  ● SYS ONLINE   │
├──────────────────────────────────────────────────────────────────────┤
│                                     Main content area                                          │
└──────────────────────────────────────────────────────────────────────┘
Element Function
[ Mixer ] / [ Emphasizer ] Tab switcher — state in each tab is preserved when switching
[◐ DARK / LIGHT] Flip-switch theme toggle
● SYS ONLINE Backend health indicator — polls every 15 seconds

FT Mixer

Layout

┌──────────┬──────────┬──────────┬──────────┐
│     IMG 01   │    IMG 02    │     IMG 03  │    IMG 04    │  ← Input channels
│    Spatial   │    Spatial   │    Spatial  │    Spatial   │
│    Freq      │    Freq      │    Freq     │    Freq      │
└──────────┴──────────┴──────────┴──────────┘
┌────────────────────────────┐  ┌───────────┐
│      OUTPUT 1     │     OUTPUT 2     │  │   Controls    │
└────────────────────────────┘  └───────────┘

Loading Images

  • Double-click any input slot to open the file browser
  • Drag and drop an image file directly onto any slot
  • Supported formats: PNG, JPEG, BMP, TIFF, WEBP
  • Images are automatically converted to grayscale

Display vs Mix Role

Each viewport has two independent controls:

Control Location Effect
Display dropdown (bottom of slot) Viewport footer What you see in the FT panel. Has no effect on the mix output.
Role buttons (MAG / PHS or RE / IM) Controls sidebar What this image contributes to the IFFT reconstruction.

Brightness and Contrast

Drag on the spatial panel (left half of any slot):

  • Left / Right — adjust contrast
  • Up / Down — adjust brightness

Mix Modes

  • Some images contribute their magnitude |F(u,v)|
  • Other images contribute their phase ∠F(u,v)
  • Reconstruction: mixed_magnitude × exp(j × mixed_phase) → IFFT
  • Some images contribute their real part Re{F(u,v)}
  • Other images contribute their imaginary part Im{F(u,v)}
  • Reconstruction: mixed_real + j × mixed_imag → IFFT

Frequency Region

Enable Region Selection to restrict which frequencies participate in the mix:

Setting Captures Effect
Inner (Low) Centred rectangle Broad shapes, colour, overall brightness
Outer (High) Everything outside rect Fine detail, edges, texture

The region rectangle appears as a coloured overlay on all 4 FT panels simultaneously — it is always unified across images.

Classic experiment

Load a face image into IMG 01 (role: MAG) and a different face into IMG 02 (role: PHS). Set both weights to 1.0. The output will structurally resemble IMG 02 (phase carries layout) with IMG 01's frequency energy (magnitude carries intensity pattern).

Output Ports

  • Click an output monitor to make it the active target (cyan glow = active)
  • All mix results go to whichever output is currently selected
  • Click the download icon in the output header to save as PNG

FT Emphasizer

Layout

┌─────────────┐  ┌───────────────┬───────────────┐
│  Controls        │  │       Original      │  Original     │
│  (sidebar)       │  │       Spatial       │  FT           │
│                  │  ├───────────────┼───────────────┤
│                  │  │       Transformed   │  FT of        │
│                  │  │       Spatial       │  Transformed  │
└─────────────┘  └───────────────┴───────────────┘

Domain Toggle

The Apply Action On control is the centrepiece:

  • Your action modifies the image f(x,y)
  • Top row shows the original image and its FT
  • Bottom row shows the transformed image and its FT
  • Watch the FT react to your spatial operation
  • Your action modifies the FT directly F(u,v)
  • Top row shows the original FT and its IFFT (the image)
  • Bottom row shows the transformed FT and its reconstruction
  • Watch the image change as you manipulate the spectrum

Actions

Action What it does Key FT insight
Shift Slides the image Magnitude unchanged; only phase rotates
Complex Exp. Multiply Imposes a wave on the image Shifts the entire FT to a new frequency location
Stretch Scales image axes FT compresses inversely (scaling theorem)
Mirror Flips the image FT flips correspondingly
Make Even (image + mirror) / 2 FT becomes purely real
Make Odd (image − mirror) / 2 FT becomes purely imaginary
Rotate Rotates N degrees FT rotates by the same angle
Differentiate Detects edges FT boosted at high frequencies
Integrate Running sum FT suppressed at high frequencies (blurring)
Window Function Smooth fade to zero at edges Reduces spectral leakage via convolution theorem

Repeated Fourier

The FT times slider applies N additional FFTs after your chosen action:

  • 0 — no extra Fourier (action only)
  • 1 — one extra FFT applied to the result
  • 4 — many images converge to a rotated/scaled version of themselves

Educational InfoCards

Every action includes a collapsible card:

▼  What does this do?
────────────────────────────────────────────
 f(x,y) Spatial    ↔    F(u,v) Frequency
 Plain English          Plain English
 explanation            explanation
────────────────────────────────────────────
 ⚡ FT Duality
 The deeper mathematical relationship
 between the two domains

Click "What does this do?" to expand/collapse.