## Sampling theory, the best explanation you’ve ever heard—Part 1

I’ll start by giving away secrets first: Individual digital samples are impulses. Not bandlimited impulses, ideal ones. We know what lies between samples—virtual zero samples. Audio samples don’t represent the source audio. They represent a modulated version of the audio. … Continue reading

Posted in Digital Audio, Sampling Theory | Tagged | 4 Comments

## Sampling theory, the best explanation you’ve ever heard—Prologue

I’ve been working on a new video, with the goal of giving the best explanation of digital sampling you’ve ever heard. The catch is I started on it three years ago. I’m not that slow, it’s just that I’ve been … Continue reading

## Amp simulation oversampling

In tandem with our last article on Guitar amp simulation, this article gives a step by step view of the sampling and rate conversion processes, with a look at the frequency spectrum. From guitar to digital The first two charts embody the … Continue reading

## Guitar amp simulation

In this article, I’ll sketch a basic guitar amp simulator. For one, questions on the topic come up often, and also, it will be a good example of a typical use of working at a higher sample rate. The most … Continue reading

Posted in Aliasing, Digital Audio, Sample Rate Conversion | 3 Comments

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

## 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 | 15 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

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

## 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