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Improve decision boundary between time domain and frequency filtering #273

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merged 6 commits into from
May 3, 2019
Merged

Improve decision boundary between time domain and frequency filtering #273

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82c111c
Use constant for small filter cutoff size
galenlynch Apr 1, 2019
c0eb33d
Change heuristic for choice between fft and time domain filtering
galenlynch Apr 1, 2019
fc03a14
Make nfft cost estimation for overlap-save algorithm more accurate
galenlynch Apr 1, 2019
a59adfb
Use generated function instead of eval
galenlynch Apr 2, 2019
82ed0fb
Change cutoff for using time domain filtering over fft
galenlynch Apr 2, 2019
6aa2ca3
Revert "Use generated function instead of eval"
galenlynch May 3, 2019
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39 changes: 19 additions & 20 deletions src/Filters/filt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -386,11 +386,13 @@ function filt_stepstate(f::SecondOrderSections{T}) where T
si
end

const SMALL_FILT_CUTOFF = 54

#
# filt implementation for FIR filters (faster than Base)
#

for n = 2:15
for n = 2:SMALL_FILT_CUTOFF
silen = n-1
si = [Symbol("si$i") for i = 1:silen]
@eval function filt!(out, b::NTuple{$n,T}, x) where T
Expand All @@ -412,7 +414,7 @@ for n = 2:15
end

let chain = :(throw(ArgumentError("invalid tuple size")))
for n = 15:-1:2
for n = SMALL_FILT_CUTOFF:-1:2
chain = quote
if length(h) == $n
filt!(out, ($([:(h[$i]) for i = 1:n]...),), x)
Expand Down Expand Up @@ -452,7 +454,7 @@ end
function _tdfilt!(out::AbstractArray, h::AbstractVector, x::AbstractArray)
if length(h) == 1
return mul!(out, h[1], x)
elseif length(h) <= 15
elseif length(h) <= SMALL_FILT_CUTOFF
return small_filt!(out, h, x)
end

Expand Down Expand Up @@ -484,21 +486,22 @@ filt(h::AbstractArray, x::AbstractArray) =
# fftfilt and filt
#

# Number of real operations required for overlap-save with nfft = 2^pow2 and filter
# length nb
os_fft_complexity(pow2, nb) = 4 * (2 ^ pow2 * (pow2 + 1)) / (2 ^ pow2 - nb + 1)
# Rough estimate of number of multiplications per output sample
os_fft_complexity(nfft, nb) = (nfft * log2(nfft) + nfft) / (nfft - nb + 1)

# Determine optimal length of the FFT for fftfilt
function optimalfftfiltlength(nb, nx)
first_pow2 = ceil(Int, log2(nb))
last_pow2 = ceil(Int, log2(nx + nb - 1))
complexities = os_fft_complexity.(first_pow2:last_pow2, nb)

# Find power of 2 with least complexity relative to the first power of 2
relative_ind_best_pow2 = argmin(complexities)

best_pow2 = first_pow2 + relative_ind_best_pow2 - 1
nfft = 2 ^ best_pow2
last_complexity = os_fft_complexity(2 ^ first_pow2, nb)
pow2 = first_pow2 + 1
while pow2 <= last_pow2
new_complexity = os_fft_complexity(2 ^ pow2, nb)
new_complexity > last_complexity && break
last_complexity = new_complexity
pow2 += 1
end
nfft = pow2 > last_pow2 ? 2 ^ last_pow2 : 2 ^ (pow2 - 1)

L = nfft - nb + 1
if L > nx
Expand Down Expand Up @@ -605,14 +608,10 @@ function filt_choose_alg!(
x::AbstractArray{<:Real}
)
nb = length(b)
nx = size(x, 1)

filtops_per_sample = min(nx, nb)

nfft = optimalfftfiltlength(nb, nx)
fftops_per_sample = os_fft_complexity(log2(nfft), nb)

if filtops_per_sample > fftops_per_sample
if nb > SMALL_FILT_CUTOFF
nx = size(x, 1)
nfft = optimalfftfiltlength(nb, nx)
_fftfilt!(out, b, x, nfft)
else
_tdfilt!(out, b, x)
Expand Down