delay

FFT-based delaying of a vector.

Namespace: dsp::fourier

Prototype

Vector<T> delay(const Vector<T> &x, float τ)

Parameters

x	Vector of samples.
τ	Delay to be applied, in number of samples (can be positive or negative, and not necessarily an integer).

Returns

Time shifted vector.

Description

Apply a fractionnal delay to the input signal: \[ y_k = x_{k-\tau} \]

The delay can be positive (to effectively delay the signal), or negative (to have the signal earlier).

Note

If the request delay is an integer, a simple shift of the vector is done. Otherwise, the delay is applied in the frequency domain (after the input signal has been zero-padded so as to mitigate border effects): \[ Y_n = X_n \cdot e^{\frac{-2\pi\mathbf{i}\tau \cdot n}{N}} \]

Example


  // Signal test : gaussienne
  soit x = siggauss(20);

  // Délais de 1 échantillons
  soit x1 = délais(x, 1),
  // Délais de 1.5 échantillons
       x2 = délais(x, 1.5),
  // Avance de 1  échantillons
       x3 = délais(x, -1);

  Figure f;
  f.plot(x,  "b-o", "x");
  f.plot(x1, "g-o", "x1 (+1)");
  f.plot(x2, "m-o", "x2 (+1,5)");
  f.plot(x3, "c-o", "x3 (-1)");