Low-pass, high-pass, and band-pass filter responses
A low-pass filter passes frequencies below its cutoff frequency (-3 dB point) and attenuates higher frequencies, rolling off at 20 dB per decade. A high-pass filter does the opposite, passing high frequencies and blocking low ones. A band-pass filter combines the two, allowing only a narrow band of frequencies to pass, useful for tuning radios and isolating signals. The Bode plot shows magnitude (how much the signal is amplified or reduced) and phase shift (how much the output lags the input) across frequency, making it easy to see the filter's effect across the spectrum.
Phase shift and group delay in filtering
Beyond amplitude, filters shift the phase of the signal. A low-pass filter causes output to lag input increasingly as frequency rises. At the cutoff frequency, the phase shift is 45 degrees (first-order) or steeper (higher order). High phase shift can distort pulse shapes and cause ringing in time-domain transients. The group delay (the slope of phase versus frequency) describes how much a signal pulse is delayed. A linear phase filter (constant group delay) preserves pulse shape; a nonlinear phase filter distorts it. Filter order (steepness of the roll-off) trades off complexity for better frequency rejection and steeper phase change.