Every filter page draws seven views of the same filter. They look different but describe one thing — how the circuit treats each frequency. Below, each plot is explained with a live example: a 2nd-order low-pass, f₀ = 1 kHz, Q = 2.

1 · Bode Magnitude

Gain (output ÷ input) in decibels versus frequency on a log scale. 0 dB = unity (output equals input); −6 dB ≈ half the amplitude; −20 dB = one tenth; −40 dB = one hundredth.

How to read it:

The flat region is the passband (frequencies the filter lets through).
The −3 dB point marks the cutoff frequency f_c (half power).
Past cutoff the curve falls at a fixed slope: −20 dB/decade per order (a 2nd-order filter rolls off at −40 dB/dec).
A bump near cutoff is a resonant peak — it appears when Q > 0.707, growing taller and sharper with Q.

2 · Bode Phase

How much the filter delays each frequency, in degrees. Every pole adds up to −90° of lag, every zero up to +90°. A 2nd-order low-pass swings from 0° in the passband to −180° in the stopband, passing through exactly −90° at f_c. Phase matters when you cascade stages or care about preserving a waveform's shape.

3 · Group Delay

The time each frequency is delayed, in seconds — measured as the negative slope of the phase curve (τ_g = −dφ/dω). Where Bode phase tells you the angle, group delay turns that into an actual lag a signal experiences.

How to read it:

Flat group delay across the passband means every frequency is held back by the same amount, so a waveform passes through with its shape intact — exactly what you want for audio and data. (Bessel filters are chosen for the flattest delay; Butterworth is gently humped.)
A peak near f_c means frequencies around resonance are delayed more than the rest. It grows taller and narrower with Q — the same energy storage that makes the step response ring, seen here as excess delay.

4 · Nyquist Diagram

The same transfer function drawn as a path in the complex plane: each point is H(jω) for one frequency — real part on x, imaginary part on y. Distance from the origin = gain; angle from the +x axis = phase. As frequency rises, the dot traces the curve. It's the classic tool for feedback-stability analysis (how the curve wraps the −1 point) and gives an at-a-glance feel for how gain and phase move together.

5 · Pole-Zero Map

The transfer function stripped to its roots: poles (denominator roots, drawn ✕) and zeros (numerator roots, drawn ○) on the complex plane — real part σ across, imaginary part jω up, both in Hz. Everything the other plots show is set by where these sit.

How to read it:

Poles must be in the left half-plane (σ < 0). Distance from the origin ≈ f₀.
The angle of a pole pair encodes Q: poles hugging the jω axis (nearly vertical) = high Q, sharp resonance, long ringing; poles out on the real axis = overdamped, no ringing.
Zeros mark frequencies the filter nulls — a notch puts a zero on the jω axis, a high-pass puts zeros at the origin. Our example low-pass has two complex-conjugate poles and no zeros.

6 · Impulse Response

The output when the input is a single infinitely-short spike. It reveals the filter's natural behaviour: a low-Q filter rises and decays smoothly; a high-Q filter rings as it settles. A vertical δ(t) marker at t = 0 means the filter passes part of the input straight through (high-pass, band-stop, all-pass) — only the smooth part after it is plotted.

7 · Step Response

The output when the input jumps from 0 to 1 and stays — the most intuitive view. Read off:

Rise time — how quickly it reaches the final value.
Overshoot — how far it shoots past before settling; it grows with Q. Q < 0.5 (overdamped) never overshoots; Q = 0.707 (Butterworth) is fastest with essentially none; higher Q overshoots and rings.
Settling — how long the ringing takes to die out.

The same low-pass at three Q values — watch overshoot and ringing grow with Q:

Quick reference

Cutoff f_c: where Bode magnitude crosses −3 dB.
Order: rolloff slope ÷ 20 dB/dec (also the total phase change ÷ 90°).
Q: peak height in Bode, group-delay peak at f₀, pole angle (closer to the jω axis = higher), and overshoot/ringing in the step response.
Stability & delay: every pole left of the jω axis = stable; flat group delay = the waveform keeps its shape (linear phase). Zeros on the jω axis mark notched-out frequencies.
Filter type: low-pass passes lows (falls on the right); high-pass passes highs (falls on the left); band-pass peaks in the middle; band-stop/notch dips in the middle.