sigma_delta

Builtin index · Signal processing

result = sigma_delta(x)

Input: x · Output: result

What it is

x: a length-N vector or Signal.

Overloads

One call shape — this function is not overloaded.

Code	Input	Output	Description
`result = sigma_delta(x)`	`x` vector or Signalnot documented yet	`Signal` Signalpreserving `x`'s `Fs` when it's a `Signal`	Returns a same-length vector or `Signal` (preserving `x`'s `Fs` when it's a `Signal`), each sample `+1`/`-1`. First-order (error-feedback) 1-bit noise-shaping quantizer: binarizes `x`, pushing quantization error to higher frequencies instead of spreading it evenly like plain `sign(x)` — the technique behind "DIBS-ΔΣ" excitation signals (`multisine(...)`

Examples

From the documentation, and run by the build -- the output and the figure below are what the engine actually produced. Simplest first.

fs = 1000
tone = sine(50, fs, 20)
bits = sigma_delta(tone)            # 1-bit noise-shaping quantizer

print("sigma_delta output range: [{min(bits)}, {max(bits)}]")

s = signal(0 to 9, 10)
trimmed = signal_slice_time(s, 0.2, 0.6)   # same operation `cut` is the friendlier name for

print("signal_slice_time(0.2, 0.6) -> {trimmed}")

output

sigma_delta output range: [-1, 1]
signal_slice_time(0.2, 0.6) -> signal(Fs=10) [2, 3, 4, 5, 6]

from signal-processing

How it works

sigma_delta(x) — a first-order (error-feedback) 1-bit noise-shaping quantizer: exact 1-bit binarization of x that pushes quantization error to higher frequencies instead of spreading it evenly (sign(x)'s own behavior) — the standard technique behind "DIBS-ΔΣ" excitation signals (multisine(...) |> sigma_delta) and 1-bit DACs generally. A signal's own Fs survives (same convention as diff/cumsum) since this doesn't change the sample rate, only re-quantizes the values.

From the note above this builtin in the interpreter, where the reasoning was written down as it was built.