Tapped Delay Line in O(1)

The class Tapped Delay Line implements a Tapped Delay Line (TDL), a fundamental structure in digital filter theory. A TDL delays an input signal by a number of samples and exposes each delayed version as an output

In this implementation, the TDL is backed by a circular buffer. As a result, both enqueue and dequeue operations run in constant time O(1), making integer delays highly efficient.

A delay of one sample is denoted \(z^{-1}\) , while a delay of \(N\) samples is denoted \(z^{-N}\) consistent with z-transform notation in digital signal processing.

To use a TDL, create an instance of qlibs::tdl and configure it using either the constructor or qlibs::tdl::setup(). During setup you specify both the number of delay taps and their initial values. Once configured, samples of the input signal can be inserted using qlibs::tdl::insertSample() (or the function-call operator).

You can access specific delayed samples via:

• qlibs::tdl::getOldest() - retrieves the oldest sample (tap \(z^{-N}\))
• qlibs::tdl::getAtIndex() — retrieves the sample at tap \(z^{-i}\)
• The index operator delay[i] — equivalent to getAtIndex(i)

Because of its versatility, the qlibs::tdl class is a core component in higher-level modules such as qlibs::smoother and qlibs::ltisys.

Example : Instantiating a TDL with 256 delay taps

real_t storage[ 256 ] = { 0.0f };
tdl delay( storage );

Insert new samples:

delay.insertSample( 2.5 );
delay.insertSample( -2.3 );
delay( 4.8 ); // same as delay.insertSample( 4.8 )

Retrieve delayed samples:

auto d3 = delay[ 3 ]; // get delay at t-3, same as delay.getAtIndex( 3 )
auto dOldest = delay.getOldest(); // get the oldest sample at t-N