fwht function

Fast Walsh-Hadamard Transform

Compute the (inverse) Fast Walsh-Hadamard transform of a signal.

ifwht(x, n = NROW(x), ordering = c("sequency", "hadamard", "dyadic"))

fwht(x, n = NROW(x), ordering = c("sequency", "hadamard", "dyadic"))

Arguments

• x: input data, specified as a numeric vector or matrix. In case of a vector it represents a single signal; in case of a matrix each column is a signal. fwht operates only on signals with length equal to a power of 2. If the length of x is less than a power of 2, its length is padded with zeros to the next greater power of two before processing.

• n: transform length, specified as a positive integer scalar. Default: NROW(x).

• ordering: order of the Walsh-Hadamard transform coefficients, one of:

  • "sequency": (Default) Coefficients in order of increasing sequency value, where each row has an additional zero crossing.
  • "hadamard": Coefficients in normal Hadamard order
  • "dyadic": Coefficients in Gray code order, where a single bit change occurs from one coefficient to the next

Returns

(Inverse) Fast Walsh Hadamard transform, returned as a vector or matrix.

Examples

x <- c(19, -1, 11, -9, -7, 13, -15, 5)
X <- fwht(x)
all.equal(x, ifwht(X))

References

https://en.wikipedia.org/wiki/Hadamard_transform

https://en.wikipedia.org/wiki/Fast_Walsh-Hadamard_transform

Author(s)

Mike Miller.

Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com .