21.3.4  Performing thresholding operations on an array

The threshold command changes data in an array by raising (or lowering) the values to meet a given threshold.

• threshold takes two mandatory arguments and two optional arguments:
  • v, an array (vector or matrix) of real or complex numbers.
  • a bound specification, which can be one of: This can be either:
    • b=b₀ for real numbers b and b₀.
    • b, a real number (equivalent to b=b).
    • [l=l₀,u=u₀], for real numbers l,l₀,u,u₀.
    • [l,u], a list of two real numbers (equivalent to [l=l,u=u]).
  • Optionally ’≺’, a quoted comparison operator, one of ’<’, ’<=’, ’>’, ’>=’ (by default ’<’).
  • Optionally, abs=bool, where bool is either true or false (by default abs=false). If abs=true, then the components of v must be real.
• threshold(v,b=b₀ ⟨,′≺′ ⟩) returns the array w of the same dimensions as v whose kth component is:

  wk=	⎧ ⎨ ⎩       b0, vk ≺ b,       vk, otherwise

  when v_k is real and

  wk=	⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩       b0 vk |vk| , |vk| ≺ b,       vk, otherwise

  when v_k is complex; for k=0,1,…,size(v)−1.
• threshold(v,b=b₀ ⟨,≺ ⟩,abs=true) returns the vector w whose kth component is:

  wk=	⎧ ⎪ ⎨ ⎪ ⎩       b0, |vk| ≺ b  and  vk>0,       −b0, |vk| ≺ b  and  vk<0       vk, otherwise

• threshold(v,[l=l₀,u=u₀] ⟨,≺ ⟩) returns the vector w whose kth component is:

  wk=	⎧ ⎪ ⎨ ⎪ ⎩       u0, u ≺ vk,       l0, vk ≺ l       vk, otherwise

  when v_k is real and

  wk=	⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩       u0 vk |vk| , u ≺ |vk|,       l0 vk |vk| , |vk| ≺ l,       vk, otherwise

  when v_k is complex; for k=0,1,…,size(v)−1.

Examples

In the following example, a square-like signal is created from a sine wave by clipping sample values.