An image is a signal, not a picture

The single most useful reframing in this whole field: a photograph is a 2-D signal — a function of two spatial variables that happens to be sampled on a grid. The moment you accept that, tools you already know from audio transfer over intact.

The transfer table is almost embarrassing in how well it holds:

· Convolution — same operation, two dimensions instead of one.
· Frequency / spectrum — same. A photo has spatial frequencies; sharp edges and fine textures contain high frequencies.
· Low-pass filter — blur.
· High-pass filter — edge emphasis.
· High-frequency emphasis — many sharpening filters add a high-pass detail signal back to the image; they cannot restore detail that was never captured.
· Sampling theory — the Nyquist limit applies in each image axis, and aliasing is the same disease.

# 2-D convolution — the engine behind nearly every classic filter
def convolve(img, k):
    kh, kw = k.shape
    ph, pw = kh // 2, kw // 2
    pad = np.pad(img, ((ph, ph), (pw, pw)), mode='edge')
    out = np.zeros_like(img, dtype=float)
    for y in range(img.shape[0]):
        for x in range(img.shape[1]):
            out[y, x] = (pad[y:y+kh, x:x+kw] * k).sum()
    return out

# The kernel IS the filter. Examples:
#   box 3x3        -> blur
#   gaussian       -> nicer blur (no ringing)
#   [-1,0,1]       -> horizontal derivative (responds to vertical edges)
#   laplacian      -> edges in all directions

And aliasing is not an abstract worry — it is the moiré on a striped shirt, the shimmer on a receding fence, the jaggies on a thin line. All three are the same thing: image detail above the sampling grid's Nyquist limit folding into false lower-frequency patterns.