Design 'FIR' filter using firls — design_filter

Design 'FIR' filter using firls

Usage

design_filter_fir(
  sample_rate,
  filter_order = NA,
  data_size = NA,
  high_pass_freq = NA,
  high_pass_trans_freq = NA,
  low_pass_freq = NA,
  low_pass_trans_freq = NA,
  stopband_attenuation = 40,
  scale = TRUE,
  method = c("kaiser", "firls", "remez")
)

Arguments

sample_rate: sampling frequency
filter_order: filter order, leave NA (default) if undecided
data_size: minimum length of data to apply the filter, used to decide the maximum filter order. For 'FIR' filter, data length must be greater than 3xfilter_order
high_pass_freq: high-pass frequency; default is NA (no high-pass filter will be applied)
high_pass_trans_freq: high-pass frequency band-width; default is automatically inferred from data size. Frequency high_pass_freq - high_pass_trans_freq is the corner of the stop-band
low_pass_freq: low-pass frequency; default is NA (no low-pass filter will be applied)
low_pass_trans_freq: low-pass frequency band-width; default is automatically inferred from data size. Frequency low_pass_freq + low_pass_trans_freq is the corner of the stop-band
stopband_attenuation: allowable power attenuation (in decibel) at transition frequency; default is 40 dB.
scale: whether to scale the filter for unity gain
method: method to generate 'FIR' filter, default is using kaiser estimate, other choices are firls (with hamming window) and remez design.

Value

'FIR' filter in 'Arma' form.

Details

Filter type is determined from high_pass_freq and low_pass_freq. High-pass frequency is ignored if high_pass_freq is NA, hence the filter is low-pass filter. When low_pass_freq is NA, then the filter is high-pass filter. When both high_pass_freq and low_pass_freq are valid (positive, less than 'Nyquist'), then the filter is a band-pass filter if band-pass is less than low-pass frequency, otherwise the filter is band-stop.

Although the peak amplitudes are set at 1 by low_pass_freq and high_pass_freq, the transition from peak amplitude to zero require a transition, which is tricky but also important to set. When 'FIR' filters have too steep transition boundaries, the filter tends to have ripples in peak amplitude, introducing artifacts to the final signals. When the filter is too flat, components from unwanted frequencies may also get aliased into the filtered signals. Ideally, the transition bandwidth cannot be too steep nor too flat. In this function, users may control the transition frequency bandwidths via low_pass_trans_freq and high_pass_trans_freq. The power at the end of transition is defined by stopband_attenuation, with default value of 40 (i.e. -40 dB, this number is automatically negated during the calculation). By design, a low-pass 5 Hz filter with 1 Hz transition bandwidth results in around -40 dB power at 6 Hz.

Examples


# ---- Basic -----------------------------

sample_rate <- 500
data_size <- 1000

# low-pass at 5 Hz, with auto transition bandwidth
# from kaiser's method, with default stopband attenuation = 40 dB
filter <- design_filter_fir(
  low_pass_freq = 5,
  sample_rate = sample_rate,
  data_size = data_size
)

# Passband ripple is around 0.08 dB
# stopband attenuation is around 40 dB
print(filter)
#> <FIR filter>
#>   Type : low
#>   Method: kaiser
#>   Order: 332
#>   Magnitude:
#>     Freq=5 Hz, mag=-0.1005 dB (expected=-0.0873 dB)
#>     Freq=8.4 Hz, mag=-40.92 dB (expected=-40 dB)
#>   Reciprocal condition number: 1 > .Machine$double.eps

diagnose_filter(
  filter$b, filter$a,
  fs = sample_rate,
  n = data_size,
  cutoffs = c(-3, -6, -40),
  vlines = 5
)


# ---- Advanced ---------------------------------------------

sample_rate <- 500
data_size <- 1000

# Rejecting 3-8 Hz, with transition bandwidth 0.5 Hz at both ends
# Using least-square (firls) to generate FIR filter
# Suggesting the filter order n=160
filter <- design_filter_fir(
  low_pass_freq = 3, low_pass_trans_freq = 0.5,
  high_pass_freq = 8, high_pass_trans_freq = 0.5,
  filter_order = 160,
  sample_rate = sample_rate,
  data_size = data_size,
  method = "firls"
)

#
print(filter)
#> <FIR filter>
#>   Type : stop
#>   Method: firls
#>   Order: 160
#>   Magnitude:
#>     Freq=3 Hz, mag=-5.137 dB (expected=-0.0873 dB)
#>     Freq=8 Hz, mag=-5.196 dB (expected=-0.0873 dB)
#>     Freq=3.5 Hz, mag=-6.376 dB (expected=-40 dB)
#>     Freq=7.5 Hz, mag=-6.44 dB (expected=-40 dB)
#>   Reciprocal condition number: 1 > .Machine$double.eps

diagnose_filter(
  filter$b, filter$a,
  fs = sample_rate,
  n = data_size,
  cutoffs = c(-1, -40),
  vlines = c(3, 8)
)