gsignal (version 0.3-1)

fht: Fast Hartley Transform

Description

Compute the (inverse) Hartley transform of a signal using FFT

Usage

fht(x, n = NROW(x))
ifht(x, n = NROW(x))

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.

n

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

Value

(inverse) Hartley transform, returned as a vector or matrix.

Details

The Hartley transform is an integral transform closely related to the Fourier transform, but which transforms real-valued functions to real-valued functions. Compared to the Fourier transform, the Hartley transform has the advantages of transforming real functions to real functions (as opposed to requiring complex numbers) and of being its own inverse [1].

This function implements the Hartley transform by calculating the difference between the real- and imaginary-valued parts of the Fourier-transformed signal [1]. The forward and inverse Hartley transforms are the same (except for a scale factor of 1/N for the inverse Hartley transform), but implemented using different functions.

References

[1] https://en.wikipedia.org/wiki/Hartley_transform

See Also

fft

Examples

# NOT RUN {
# FHT of a 2.5 Hz signal with offset
fs <- 100
secs <- 10
freq <- 2.5
t <- seq(0, secs - 1 / fs, 1 / fs)
x <- 5 * t + 50 * cos(freq * 2 * pi * t)
X <- fht(x)
op <- par(mfrow = c(2, 1))
plot(t, x, type = "l", xlab = "", ylab = "", main = "Signal")
f <- seq(0, fs - (1 / fs), length.out = length(t))
to <- which(f >= 5)[1]
plot(f[1:to], X[1:to], type = "l", xlab = "", ylab = "",
     main = "Hartley Transform")
par(op)

# }