R: Make a digital filter

makeFilter {oce} | R Documentation

## Make a digital filter

### Description

The filter is suitable for use by `filter`, `convolve` or (for the `asKernal=TRUE` case) with `kernapply`. Note that `convolve` should be faster than `filter`, but it cannot be used if the time series has missing values. For the Blackman-Harris filter, the half-power frequency is at `1/m` cycles per time unit, as shown in the “Examples” section. When using `filter` or `kernapply` with these filters, use `circular=TRUE`.

### Usage

    makeFilter(type = c("blackman-harris", "rectangular", "hamming", "hann"),
      m, asKernel = TRUE)

### Arguments

`type` | a string indicating the type of filter to use. (See Harris (1978) for a comparison of these and similar filters.) `"blackman-harris"` yields a modified raised-cosine filter designated as "4-Term (-92 dB) Blackman-Harris" by Harris (1978; coefficients given in the table on page 65). This is also called "minimum 4-sample Blackman Harris" by that author, in his Table 1, which lists figures of merit as follows: highest side lobe level -92dB; side lobe fall off -6 db/octave; coherent gain 0.36; equivalent noise bandwidth 2.00 bins; 3.0-dB bandwidth 1.90 bins; scallop loss 0.83 dB; worst case process loss 3.85 dB; 6.0-db bandwidth 2.72 bins; overlap correlation 46 percent for 75% overlap and 3.8 for 50% overlap. Note that the equivalent noise bandwidth is the width of a spectral peak, so that a value of 2 indicates a cutoff frequency of `1/m`, where `m` is as given below. `"rectangular"` for a flat filter. (This is just for convenience. Note that `kernel("daniell",....)` gives the same result, in kernel form.) `"hamming"` for a Hamming filter (a raised-cosine that does not taper to zero at the ends) `"hann"` (a raised cosine that tapers to zero at the ends).
`m` | length of filter. This should be an odd number, for any non-rectangular filter.
`asKernel` | boolean, set to `TRUE` to get a smoothing kernel for the return value.

### Value

If `asKernel` is `FALSE`, this returns a list of filter coefficients, symmetric about the midpoint and summing to 1. These may be used with `filter`, which should be provided with argument `circular=TRUE` to avoid phase offsets. If `asKernel` is `TRUE`, the return value is a smoothing kernel, which can be applied to a timeseries with `kernapply`, whose bandwidth can be determined with `bandwidth.kernel`, and which has both print and plot methods.

### Author(s)

Dan Kelley

### References

F. J. Harris, 1978. On the use of windows for harmonic analysis with the discrete Fourier Transform. Proceedings of the IEEE, 66(1), 51-83 (http://web.mit.edu/xiphmont/Public/windows.pdf.)

### Examples

    library(oce)

    # 1. Demonstrate step-function response
    y <- c(rep(1, 10), rep(-1, 10))
    x <- seq_along(y)
    plot(x, y, type='o', ylim=c(-1.05, 1.05))
    BH <- makeFilter("blackman-harris", 11, asKernel=FALSE)
    H <- makeFilter("hamming", 11, asKernel=FALSE)
    yBH <- stats::filter(y, BH)
    points(x, yBH, col=2, type='o')
    yH <- stats::filter(y, H)
    points(yH, col=3, type='o')
    legend("topright", col=1:3, cex=2/3, pch=1,
           legend=c("input", "Blackman Harris", "Hamming"))

    # 2. Show theoretical and practical filter gain, where
    #    the latter is based on random white noise, and
    #    includes a particular value for the spans
    #    argument of spectrum(), etc.
    ## Not run:
    # need signal package for this example
    r <- rnorm(2048)
    rh <- stats::filter(r, H)
    rh <- rh[is.finite(rh)] # kludge to remove NA at start/end
    sR <- spectrum(r, plot=FALSE, spans=c(11, 5, 3))
    sRH <- spectrum(rh, plot=FALSE, spans=c(11, 5, 3))
    par(mfrow=c(2, 1), mar=c(3, 3, 1, 1), mgp=c(2, 0.7, 0))
    plot(sR$freq, sRH$spec/sR$spec, xlab="Frequency", ylab="Power Transfer",
         type='l', lwd=5, col='gray')
    theory <- freqz(H, n=seq(0,pi,length.out=100))
    # Note we must square the modulus for the power spectrum
    lines(theory$f/pi/2, Mod(theory$h)^2, lwd=1, col='red')
    grid()
    legend("topright", col=c("gray", "red"), lwd=c(5, 1), cex=2/3,
           legend=c("Practical", "Theory"), bg="white")
    plot(log10(sR$freq), log10(sRH$spec/sR$spec),
         xlab="log10 Frequency", ylab="log10 Power Transfer",
         type='l', lwd=5, col='gray')
    theory <- freqz(H, n=seq(0,pi,length.out=100))
    # Note we must square the modulus for the power spectrum
    lines(log10(theory$f/pi/2), log10(Mod(theory$h)^2), lwd=1, col='red')
    grid()
    legend("topright", col=c("gray", "red"), lwd=c(5, 1), cex=2/3,
           legend=c("Practical", "Theory"), bg="white")

    ## End(Not run)

[Package oce version 1.1-1 Index]