Bode plot · Frequency response · Pole-zero · FIR/IIR · Real-time filtering
Digital filters are at the core of all modern signal processing — from audio equalisation and speech recognition to medical imaging and software-defined radio. This simulator lets you design FIR and IIR filters interactively, watching the Bode plot (magnitude and phase) and pole-zero diagram update in real time as you move the sliders.
Digital filters selectively pass or block frequency ranges. FIR (Finite Impulse Response) filters use only feedforward taps — they are always stable and have linear phase (meaning all frequencies are delayed equally, preserving waveform shape). IIR (Infinite Impulse Response) filters use feedback, requiring fewer taps to achieve the same roll-off steepness, but they can become unstable (poles must stay inside the unit circle) and introduce non-linear phase. The Bode plot shows magnitude response (how much each frequency is attenuated) and phase response (how much it is delayed). The pole-zero diagram in the Z-plane shows stability: poles outside the unit circle → unstable.
Select a filter type (low-pass, high-pass, band-pass) and design method (FIR windowed-sinc or IIR Butterworth/Chebyshev). Move the Cutoff Frequency slider and watch the Bode plot update in real time. Increase the Filter Order to get a steeper roll-off (sharper transition from passband to stopband) at the cost of more computation. Switch to Chebyshev and adjust the ripple — you get a steeper initial roll-off in exchange for ripple in the passband. Try the white noise test signal and observe how the filter removes high or low frequencies from the waveform preview.
Your smartphone audio codec applies dozens of digital filters every millisecond — equaliser, noise cancellation, echo removal, and anti-aliasing. MP3 compression uses a 32-band polyphase filter bank to split audio into frequency subbands. The FIR windowed-sinc method was popularised by Fred Harris in his landmark 1978 IEEE paper “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform”. Modern FPGA-based software-defined radios (SDRs) run FIR filters with thousands of taps at GHz sample rates using pipelined multiplier-accumulator (MAC) units.