### Understanding the Levinson-Durbin Algorithm

Digital Signal Processing

Mathematics

I’ve recently been playing with this algorithm and wanted to do a write-up of my…

### Building a digital filter for use in synthesisers

Digital Signal Processing

State Space Representation

Digital Filters

Synthesis

This is a tutorial on how to build a digital implementation of a 2nd-order, continuously-variable filter (i.e. one where you can change the parameters runtime) that has…

### Even More Householder

Mathematics

Linear Algebra

Householder Matrix

In several previous blogs (here and here)…

### An attempt at an intuitive description of the QR decomposition using Householder reflectors

Mathematics

Linear Algebra

Householder Matrix

I really like the Householder matrix. I’ve blogged about its ability to generate an orthonormal basis containing a particular vector in a previous blog post. This blog post is a bit of a tutorial which will use the Householder matrix to perform a QR decomposition. Applying Householder reflectors to compute a QR decomposition is…

### On the perils of cross-fading loops in organ samples

Digital Signal Processing

Crossfading

Sampled Pipe Organs

One common strategy when looping problematic organ samples is to employ a cross-fade. This is an irreversible audio modification that gradually transitions the samples…

### Arbitrary polynomial-segment signal generation

Mathematics

State Space Representation

Digital Signal Processing

Synthesis

There is a tool which is part of my Open Diapason virtual organ project called “sampletune” which is designed to allow sample-set creators to tune samples by ear and save…

### Three step digital Butterworth design

Digital Signal Processing

Digital Filters

This guide omits a fair amount of detail in order to provide a fairly quick guide.

### Real-time re-sampling and linear interpolation

Digital Signal Processing

Digital Filters

Multirate Signal Processing

Resampling

*Disclaimer: I’ve intentionally tried to keep this post “non-mathy” - I want it to provide a…*

### Release alignment in sampled pipe organs – part 1

Digital Signal Processing

Sampled Pipe Organs

Crossfading

Correlation

A sample from a digital pipe organ contains at least:

### Derivation of fast DCT-4 algorithm based on DFT

Mathematics

Discrete Cosine Transform

It’s well known that an \(N\) point DCT-4 can be computed using an \(N/2\) point complex FFT. Although the algorithm is widespread, the texts which I have read on the subject have not provided the details as to how it works. I’ve been trying to…

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