Category Archives: IIR Filters

About coefficient conventions

It’s been asked many times, so it’s worth an article explaining the conventions used on this site for transfer functions, and why they may differ from what you see elsewhere. People run into this most often with biquads: I use … Continue reading

Posted in Biquads, IIR Filters | 7 Comments

Filter frequency response grapher

Here’s a tool that plots frequency response from filter coefficients. Hz linearlog 10log 2 Plot auto40 dB30 dB20 dB10 dB0 dB-10 dB-20 dB-30 dB-40 dB Max 60 dB80 dB100 dB120 dB140 dB160 dB180 dB Range a coefficients (zeros) b coefficients … Continue reading

Posted in Biquads, Filters, FIR Filters, IIR Filters, Widgets | 13 Comments

Evaluating filter frequency response

A question that pops up for many DSP-ers working with IIR and FIR filters, I think, is how to look at a filter’s frequency and phase response. For many, maybe they’ve calculated filter coefficients with something like the biquad calculator … Continue reading

Posted in Biquads, FFT, Filters, FIR Filters, IIR Filters | 27 Comments

Cascading filters

Sometimes we’d like to cascade biquads to get a higher filter order. This calculator gives the Q values for each filter to achieve Butterworth response for lowpass and highpass filters. Order: 234567891011121314151617181920 Q values: You can calculate coefficients for all biquad … Continue reading

Posted in Biquads, Filters, IIR Filters, Widgets | 32 Comments

Filters for synths—the 4-pole

The last post noted that the two most popular synthesizer filters are the 2-pole state variable, and the 4-pole “Moog style”. And we started with the state variable—simple, popular, and delivering multiple filter outputs (lowpass, bandpass…) simultaneously. Here, we’ll follow … Continue reading

Posted in Digital Audio, Filters, IIR Filters, Synthesizers | 5 Comments

Filters for synths–starting out

We haven’t developed a synth filter here yet… Filters we’ve presented Biquads. While they are useful for many simple cases of filtering, they are not a good choice for analog synthesizer emulation. Most notably, they are poorly suited to time-varying … Continue reading

Posted in Digital Audio, Filters, IIR Filters, Synthesizers | Leave a comment

Pole-Zero placement v2

Pair Pole mag Pole angle Pair Zero mag Zero angle Sample rate (Hz) linearlog Plot A new pole-zero calculator An JavaScript remake of the old Java-based pole-zero placement applet—visit that page for tips on pole-zero locations for standard biquads. The … Continue reading

Posted in Biquads, Digital Audio, Filters, IIR Filters, Widgets | 13 Comments

Biquad calculator v2

Type:lowpasshighpassbandpassnotchpeaklow shelfhigh shelfone-pole lpone-pole hp Plot:linearlog Sample rate (Hz) Fc (Hz) Q Gain (dB) Here’s an update of the biquad calculator. It adds one-pole highpass and lowpass filters, and frequency, Q, and gain sliders. The sliders cover the range of … Continue reading

Posted in Biquads, Digital Audio, Filters, IIR Filters, Widgets | 94 Comments

Envelope generators—ADSR Part 1

After discussing the exponential decay of the one-pole filter in a recent article, I couldn’t help but think about envelope generators. Besides, it would be handy to have one to test out some of these other components I’ve been writing … Continue reading

Posted in Envelope Generators, IIR Filters, Synthesizers | 1 Comment

A one-pole filter

Here’s a very simple workhorse of DSP applications—the one-pole filter. By comparison, biquads implement two zeros and two poles. You can see that our one-pole simply discards the zeros (the feed-forward delay paths) and the second pole (feedback path): We … Continue reading

Posted in DC Blocker, Digital Audio, IIR Filters, Source Code | 38 Comments