Delay Array — User Guide

What this does

Delay Array processes the selected Sound with between one and four successive two-tap FIR stages. Every stage uses the same operation:

where D is the active delay in samples. Because the current sample is subtracted from a shifted copy, the stage has zero response at DC and a repeating comb-shaped magnitude response. Multiple iterations cascade these responses, multiplying their spectral effects.

What is a delay-difference filter?

A two-tap difference filter compares two samples separated by D samples. In this script the shifted sample is the future sample x[n+D]:

The response is zero at DC and repeats zeros at integer multiples of:

The magnitude response is the same as the more familiar delayed-difference form x[n] - x[n-D]; using the future sample changes time alignment and finite-boundary behavior, not the comb magnitude.

Quick start

1. Select exactly one Sound object.
2. Run Delay_Array.praat.
3. Choose one of the six presets or Custom.
4. Choose how many stages to apply with Number_of_iterations (1–4).
5. Leave Use_ms_delay off for file-relative delays, or enable it for explicit short delays in milliseconds.
6. Set Scale_peak for the final peak-normalization target.
7. Run the script. The result remains the same duration and channel count as the input.

Delay modes

File divisor mode — default

With Use_ms_delay = Off, each active delay is derived from the total sample count:

The delay therefore scales with the duration of the selected Sound. A divisor of 2 is approximately half the file duration; a divisor of 8 is approximately one eighth. Active divisors must be greater than 1.

Millisecond mode

With Use_ms_delay = On:

The actual delay is sample-quantized, so the Info window reports both the requested millisecond value and the realized sample/millisecond value.

Cascade behavior

Each stage processes the result of the previous stage:

In frequency-domain terms, the stage responses multiply. After K stages:

Every stage contributes its own regularly spaced zeros, so combinations of delays create a denser composite notch pattern. The process is linear and time-invariant apart from the finite-length boundary at the end of the Sound.

Presets

Each named preset supplies both divisor values and millisecond values. The active set depends on Use_ms_delay.

Presets do not change Number_of_iterations, Use_ms_delay, Scale_peak, visualization, or playback.

Parameters

Finite-signal boundary

The formula is evaluated across the full Sound. Near the end, n + D may lie beyond the available samples. Praat returns zero for out-of-range self[index], so the operator becomes:

for those tail samples. This is equivalent to zero-padding the shifted branch rather than leaving the tail unprocessed or deleting it.

Visualization

When enabled, the Picture window shows:

• Source: mono display copy of the original Sound.
• Delay cascade map: one block per active stage, labelled with x[n+D] - x[n], the realized delay, and the corresponding comb-zero spacing.
• Output: mono display copy of the processed result.
• Summary: preset, delay mode, iteration count, realized delay range, comb-zero spacing range, duration, and peak target.

Source and Output use a shared amplitude scale, so their displayed amplitudes can be compared directly.

Output behavior

• The original Sound remains unchanged; processing is performed on a copy.
• Input duration and channel count are preserved.
• Each channel is filtered independently by the same cascade.
• Every active delay must be at least 1 sample and shorter than the Sound.
• The output name is <source>_delayArray_<preset>_div in divisor mode or ..._ms in millisecond mode.

Peak scaling

After all active stages, the script measures the absolute sample extremum. If the result is non-silent, it always executes Scale peak to Scale_peak.