Category Archives: Filters

Biquad formulas

Posted on January 2, 2011 by Nigel Redmon

For fixed filters, we can plug biquad coefficients into our programs. But often, we need to calculate them on the fly, to user settings or changes in sample rate. As a companion to the biquad calculator, here are the formulas … Continue reading →

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

A biquad calculator

Posted on December 20, 2010 by Nigel Redmon

Something useful: a biquad filter coefficient calculator… Continue reading →

Posted in Digital Audio, Filters, IIR Filters | 7 Comments

Sample rate conversion: down

Posted on December 20, 2010 by Nigel Redmon

In doubling the sample rate, we inserted zeros between existing samples, then used a lowpass filter to remove the resulting alias in the audio band. To resample at half the current rate, we use a lowpass filter to remove audio … Continue reading →

Posted in Aliasing, Digital Audio, Filters, Sample Rate Conversion | Leave a comment

A closer look at upsampling filters

Posted on December 11, 2010 by Nigel Redmon

Interpolation type: None Zero-order hold Linear Sinc 1 Sinc 2 Sinc 3  Show impulse response Sweep! In this demonstration, we generate a sine wave sweep from low in the audio band to near the Nyquist Frequency, which is half the … Continue reading →

Posted in Aliasing, Digital Audio, FIR Filters, Filters, Impulse Response, Sample Rate Conversion | Leave a comment

Sample rate conversion: up

Posted on December 5, 2010 by Nigel Redmon

Once we have a suitable set of FIR filter coefficients from our windowed sinc calculator, it’s time to apply them. Again, our recipe for doubling the sample rate: 1) Insert a zero between existing samples. (This is the upsampling step, … Continue reading →

Posted in Aliasing, Convolution, Digital Audio, FIR Filters, Filters, Sample Rate Conversion | 4 Comments

Building a windowed sinc filter

Posted on December 5, 2010 by Nigel Redmon

As promised, here’s our windowed sinc calculator for building a 2x oversampling filter:  Factor  Length  Rejection  Gain Notes: Use the Tab or Enter keys to effect changes (most browsers), or press Calculate. The frequency axis is in multiples of the … Continue reading →

Posted in Digital Audio, FIR Filters, Filters, Impulse Response, Sample Rate Conversion | 2 Comments

Towards practical resampling

Posted on November 23, 2010 by Nigel Redmon

In a previous article, we looked at sample rate conversion in the frequency domain. Let’s take a quick second look in the time domain as reinforcement of principles behind sample rate conversion, before developing a practical rate convertor. In an … Continue reading →

Posted in Digital Audio, FIR Filters, Filters, Impulse Response, Sample Rate Conversion | 4 Comments

The bilinear z transform

Posted on March 2, 2003 by Nigel Redmon

The bilinear transform is the most popular method of converting analog filter prototypes in the s domain to the z domain so we can implement them as digital filters. The reason we are interested in these s domain filters is … Continue reading →

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The digital state variable filter

Posted on March 2, 2003 by Nigel Redmon

The digital state variable filter was described in Hal Chamberlin’s Musical Applications of Microprocessors. Derived by straight-forward replacement of components from the analog state variable fiter with digital counterparts, the digital state variable is a popular synthesizer filter, as was its … Continue reading →

Posted in Digital Audio, Filters, IIR Filters | 1 Comment

Biquads

Posted on February 28, 2003 by Nigel Redmon

One of the most-used filter forms is the biquad. A biquad is a second order (two poles and two zeros) IIR filter. It is high enough order to be useful on its own, and—because of coefficient sensitivities in higher order … Continue reading →

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