Signals & systems

frequency response

Frequency response describes what an LTI system does to each frequency that passes through it: how much it boosts or cuts that tone (the magnitude) and how much it delays it (the phase). It's the system's equalizer curve. Plot the bass-to-treble gain of a loudspeaker and you've drawn its frequency response — a flat line means faithful reproduction, a dip at 3 kHz means that band sounds quiet.

Mathematically it is the Fourier transform of the impulse response, H(jω), and it explains the system entirely because of the golden rule: feed a pure sinusoid into an LTI system and out comes the SAME-frequency sinusoid, only rescaled in amplitude and shifted in phase. So you can characterize any LTI box by sweeping a tone generator across all frequencies and recording the gain and phase at each — exactly what a Bode plot draws. Low-pass, high-pass, band-pass and notch filters are all just different shapes of frequency response.

H(jω) = |H(jω)|·e^(j·∠H(jω))

Magnitude is usually plotted in decibels and frequency on a log axis, because hearing and most physical systems span many orders of magnitude. The 'golden rule' that a sinusoid in gives the same-frequency sinusoid out is exactly what fails for nonlinear systems, which DO create new frequencies.

Also called
H(jω)frequency-domain transfer頻響