DSF_Convolve {stream}

Apply a Filter to a Data Stream

Description

Applies a filter (i.e., a convolution with a filter kernel) to a data stream.

Usage

DSF_Convolve(
  dsd = NULL,
  dim = NULL,
  kernel = NULL,
  pre = NULL,
  post = NULL,
  na.rm = FALSE,
  replace = TRUE,
  name = NULL
)

filter_MA(width)

filter_Hamming(width)

filter_diff(lag)

filter_Sinc(fc, fs, width = NULL, bw = NULL)

pow2(x)

Arguments

dsd

A object of class DSD.

dim

columns to which the filter should be applied. Default is all columns.

kernel

filter kernel as a numeric vector of weights.

pre, post

functions to be applied before and after the convolution.

na.rm

logical; should NAs be ignored?

replace

logical; should the column be replaced or a column with the convolved column added?

name

character; the new column will be name with the old column name + ⁠_⁠ + name.

width

filter width.

lag

an integer indicating which time lag to use.

fc

cutoff frequency.

fs

sampling frequency.

bw

transition bandwidth.

x

values to be squared.

Details

A filter kernel is a vector with kernel weights. A few filter are provided.

• filter_MA(width) creates a moving average.

• filter_diff(lag) calculates lagged differences. Note that na.rm = TRUE will lead to artifacts and should not be used.

• filter_Hamming(width) creates a Hamming window.

• filter_Sinc(fc, fs, width, bw) creates a windowed-sinc filter. One of width (filter length) or bw (transition bandwidth can be used to control the filter roll-off. The relationship is width = 4/bw. See Chapter 16 in Smith (1997).

pre and post are functions that are called before and after the convolution. For example, to calculate RMS, you can use pre = pow2 and post = sqrt. pow2() is a convenience function.

Value

An object of class DSF_Convolve (subclass of DSF and DSD).

Author(s)

Michael Hahsler

References

Steven W. Smith, The Scientist and Engineer's Guide to Digital Signal Processing, California Technical Pub; 1st edition (January 1, 1997). ISBN 0966017633, URL: https://www.dspguide.com/

See Also

stats::filter provides non-streaming convolution.

Other DSF: DSF(), DSF_Downsample(), DSF_ExponentialMA(), DSF_FeatureSelection(), DSF_Func(), DSF_Scale(), DSF_dplyr()

Examples

data(presidents)

## Example 1: Create a data stream with three copies of president approval ratings.
## We will use several convolutions.
stream <- data.frame(
    approval_orig = presidents,
    approval_MA = presidents,
    approval_diff1 = presidents,
    .time = time(presidents)) %>%
  DSD_Memory()

plot(stream, dim = 1, n = 120, method = "ts")

## apply a moving average filter to dimension 1 (using the column name) and diff to dimension 3
filteredStream <- stream %>%
  DSF_Convolve(kernel = filter_MA(5), dim = "approval_orig", na.rm = TRUE) %>%
  DSF_Convolve(kernel = filter_diff(1), dim = 3)
filteredStream

## resetting the filtered stream also resets the original stream
reset_stream(filteredStream)
ps <- get_points(filteredStream, n = 120)
head(ps)

year <- ps[[".time"]]
approval <- remove_info(ps)
matplot(year, approval, type = "l", ylim = c(-20, 100))
legend("topright", colnames(approval), col = 1:3, lty = 1:3, bty = "n")

## Example 2: Create a stream with a constant sine wave and apply
## a moving average, an RMS envelope and a differences
stream <- DSD_Memory(data.frame(y = sin(seq(0, 2 * pi - (2 * pi / 100) ,
  length.out = 100))), loop = TRUE)
plot(stream, n = 200, method = "ts")

filteredStream <- stream %>%
  DSF_Convolve(kernel = filter_MA(100), dim = 1,
    replace = FALSE, name = "MA") %>%
  DSF_Convolve(kernel = filter_MA(100), pre = pow2, post = sqrt, dim = 1,
    replace = FALSE, name = "RMS") %>%
  DSF_Convolve(kernel = filter_diff(1), dim = 1,
    replace = FALSE, name = "diff1")
filteredStream

ps <- get_points(filteredStream, n = 500)
head(ps)

matplot(ps, type = "l")
legend("topright", colnames(ps), col = 1:4, lty = 1:4)

## Note that MA and RMS use a window of length 200 and are missing at the
##   beginning of the stream the window is full.

## Filters: look at different filters
filter_MA(5)
filter_diff(1)
plot(filter_Hamming(20), type = "h")
plot(filter_Sinc(10, 100, width = 20), type = "h")