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stream_filt.jl
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stream_filt.jl
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const PFB{T} = Matrix{T} # polyphase filter bank
abstract type Filter end
abstract type FIRKernel{T} end
# Single rate FIR kernel
mutable struct FIRStandard{T} <: FIRKernel{T}
h::Vector{T}
hLen::Int
end
function FIRStandard(h::Vector)
h = Compat.reverse(h, dims=1)
hLen = length(h)
FIRStandard(h, hLen)
end
# Interpolator FIR kernel
mutable struct FIRInterpolator{T} <: FIRKernel{T}
pfb::PFB{T}
interpolation::Int
Nϕ::Int
tapsPerϕ::Int
inputDeficit::Int
ϕIdx::Int
hLen::Int
end
function FIRInterpolator(h::Vector, interpolation::Integer)
pfb = taps2pfb(h, interpolation)
tapsPerϕ, Nϕ = size(pfb)
interpolation = interpolation
inputDeficit = 1
ϕIdx = 1
hLen = length(h)
FIRInterpolator(pfb, interpolation, Nϕ, tapsPerϕ, inputDeficit, ϕIdx, hLen)
end
# Decimator FIR kernel
mutable struct FIRDecimator{T} <: FIRKernel{T}
h::Vector{T}
hLen::Int
decimation::Int
inputDeficit::Int
end
function FIRDecimator(h::Vector, decimation::Integer)
h = Compat.reverse(h, dims=1)
hLen = length(h)
inputDeficit = 1
FIRDecimator(h, hLen, decimation, inputDeficit)
end
# Rational resampler FIR kernel
mutable struct FIRRational{T} <: FIRKernel{T}
pfb::PFB{T}
ratio::Rational{Int}
Nϕ::Int
ϕIdxStepSize::Int
tapsPerϕ::Int
ϕIdx::Int
inputDeficit::Int
hLen::Int
end
function FIRRational(h::Vector, ratio::Rational)
pfb = taps2pfb(h, numerator(ratio))
tapsPerϕ, Nϕ = size(pfb)
ϕIdxStepSize = mod(denominator(ratio), numerator(ratio))
ϕIdx = 1
inputDeficit = 1
hLen = length(h)
FIRRational(pfb, ratio, Nϕ, ϕIdxStepSize, tapsPerϕ, ϕIdx, inputDeficit, hLen)
end
#
# Arbitrary resampler FIR kernel
#
# This kernel is different from the others in that it has two polyphase filtlter banks.
# The the second filter bank, dpfb, is the derivative of pfb. The purpose of this is to
# allow us to compute two y values, yLower & yUpper, whitout having to advance the input
# index by 1. It makes the kernel simple by not having to store extra state in the case
# when where's at the last polphase branch and the last available input sample. By using
# a derivitive filter, we can always compute the output in that scenario.
# See section 7.6.1 in [1] for a better explanation.
mutable struct FIRArbitrary{T} <: FIRKernel{T}
rate::Float64
pfb::PFB{T}
dpfb::PFB{T}
Nϕ::Int
tapsPerϕ::Int
ϕAccumulator::Float64
ϕIdx::Int
α::Float64
Δ::Float64
inputDeficit::Int
xIdx::Int
hLen::Int
end
function FIRArbitrary(h::Vector, rate::Real, Nϕ::Integer)
dh = [diff(h); zero(eltype(h))]
pfb = taps2pfb(h, Nϕ)
dpfb = taps2pfb(dh, Nϕ)
tapsPerϕ = size(pfb, 1)
ϕAccumulator = 1.0
ϕIdx = 1
α = 0.0
Δ = Nϕ/rate
inputDeficit = 1
xIdx = 1
hLen = length(h)
FIRArbitrary(rate, pfb, dpfb, Nϕ, tapsPerϕ, ϕAccumulator, ϕIdx, α, Δ, inputDeficit, xIdx, hLen)
end
# FIRFilter - the kernel does the heavy lifting
mutable struct FIRFilter{Tk<:FIRKernel} <: Filter
kernel::Tk
history::Vector
historyLen::Int
h::Vector
end
# Constructor for single-rate, decimating, interpolating, and rational resampling filters
"""
FIRFilter(h[, ratio])
Construct a stateful FIRFilter object from the vector of filter taps `h`.
`ratio` is an optional rational integer which specifies
the input to output sample rate relationship (e.g. `147//160` for
converting recorded audio from 48 KHz to 44.1 KHz).
"""
function FIRFilter(h::Vector, resampleRatio::Rational = 1//1)
interpolation = numerator(resampleRatio)
decimation = denominator(resampleRatio)
historyLen = 0
if resampleRatio == 1 # single-rate
kernel = FIRStandard(h)
historyLen = kernel.hLen - 1
elseif interpolation == 1 # decimate
kernel = FIRDecimator(h, decimation)
historyLen = kernel.hLen - 1
elseif decimation == 1 # interpolate
kernel = FIRInterpolator(h, interpolation)
historyLen = kernel.tapsPerϕ - 1
else # rational
kernel = FIRRational(h, resampleRatio)
historyLen = kernel.tapsPerϕ - 1
end
history = zeros(historyLen)
FIRFilter(kernel, history, historyLen, h)
end
# Constructor for arbitrary resampling filter (polyphase interpolator w/ intra-phase linear interpolation)
"""
FIRFilter(h, rate[, Nϕ])
Returns a polyphase FIRFilter object from the vector of filter taps `h`.
`rate` is a floating point number that specifies the input to output
sample-rate relationship ``\\frac{fs_{out}}{fs_{in}}``. `Nϕ` is an
optional parameter which specifies the number of *phases* created from
`h`. `Nϕ` defaults to 32.
"""
function FIRFilter(h::Vector, rate::AbstractFloat, Nϕ::Integer=32)
rate > 0.0 || error("rate must be greater than 0")
kernel = FIRArbitrary(h, rate, Nϕ)
historyLen = kernel.tapsPerϕ - 1
history = zeros(historyLen)
FIRFilter(kernel, history, historyLen, h)
end
# Constructor for a resampling FIR filter, where the user needs only to set the sampling rate
function FIRFilter(rate::AbstractFloat, Nϕ::Integer=32)
h = resample_filter(rate, Nϕ)
FIRFilter(h, rate)
end
function FIRFilter(rate::Rational)
h = resample_filter(rate)
FIRFilter(h, rate)
end
#
# setphase! set's filter kernel phase index
#
function setphase!(kernel::FIRDecimator, ϕ::Real)
ϕ >= zero(ϕ) || throw(ArgumentError("ϕ must be >= 0"))
xThrowaway = round(Int, ϕ)
kernel.inputDeficit += xThrowaway
nothing
end
function setphase!(kernel::Union{FIRInterpolator, FIRRational}, ϕ::Real)
ϕ >= zero(ϕ) || throw(ArgumentError("ϕ must be >= 0"))
(ϕ, xThrowaway) = modf(ϕ)
kernel.inputDeficit += round(Int, xThrowaway)
kernel.ϕIdx = round(ϕ*(kernel.Nϕ) + 1.0)
nothing
end
function setphase!(kernel::FIRArbitrary, ϕ::Real)
ϕ >= zero(ϕ) || throw(ArgumentError("ϕ must be >= 0"))
(ϕ, xThrowaway) = modf(ϕ)
kernel.inputDeficit += round(Int, xThrowaway)
kernel.ϕAccumulator = ϕ*(kernel.Nϕ) + 1.0
kernel.ϕIdx = round(kernel.ϕAccumulator)
kernel.α = modf(kernel.ϕAccumulator)[1]
nothing
end
setphase!(self::FIRFilter, ϕ::Real) = setphase!(self.kernel, ϕ)
#
# reset! filter and its kernel to an initial state
#
# Generic case for FIRInterpolator and FIRStandard
function reset!(kernel::FIRKernel)
kernel
end
function reset!(kernel::FIRRational)
kernel.ϕIdx = 1
kernel.inputDeficit = 1
kernel
end
function reset!(kernel::FIRDecimator)
kernel.inputDeficit = 1
kernel
end
function reset!(kernel::FIRArbitrary)
kernel.ϕAccumulator = 1.0
kernel.ϕIdx = 1
kernel.α = 0.0
kernel.inputDeficit = 1
kernel.xIdx = 1
kernel
end
# For FIRFilter, set history vector to zeros of same type and required length
function reset!(self::FIRFilter)
self.history = zeros(eltype(self.history), self.historyLen)
reset!(self.kernel)
self
end
#
# taps2pfb
#
# Converts a vector of coefficients to a matrix. Each column is a filter.
# NOTE: also flips the matrix up/down so computing the dot product of a
# column with a signal vector is more efficient (since filter is convolution)
# Appends zeros if necessary.
# Example:
# julia> taps2pfb( [1:9], 4 )
# 3x4 Array{Int64,2}:
# 9 0 0 0
# 5 6 7 8
# 1 2 3 4
#
# In this example, the first phase, or ϕ, is [9, 5, 1].
function taps2pfb(h::Vector{T}, Nϕ::Integer) where T
hLen = length(h)
tapsPerϕ = ceil(Int, hLen/Nϕ)
pfbSize = tapsPerϕ * Nϕ
pfb = Matrix{T}(undef, tapsPerϕ, Nϕ)
hIdx = 1
for rowIdx in tapsPerϕ:-1:1, colIdx in 1:Nϕ
tap = hIdx > hLen ? zero(T) : h[hIdx]
@inbounds pfb[rowIdx,colIdx] = tap
hIdx += 1
end
return pfb
end
#
# Calculates the resulting length of a multirate filtering operation, given a
# FIRFilter{FIRRational} object and an input vector
#
# ( It's hard to explain how this works without a diagram )
#
function outputlength(inputlength::Integer, ratio::Rational, initialϕ::Integer)
interpolation = numerator(ratio)
decimation = denominator(ratio)
outLen = ((inputlength * interpolation) - initialϕ + 1) / decimation
ceil(Int, outLen)
end
function outputlength(kernel::FIRStandard, inputlength::Integer)
inputlength
end
function outputlength(kernel::FIRInterpolator, inputlength::Integer)
outputlength(inputlength-kernel.inputDeficit+1, kernel.interpolation//1, kernel.ϕIdx)
end
function outputlength(kernel::FIRDecimator, inputlength::Integer)
outputlength(inputlength-kernel.inputDeficit+1, 1//kernel.decimation, 1)
end
function outputlength(kernel::FIRRational, inputlength::Integer)
outputlength(inputlength-kernel.inputDeficit+1, kernel.ratio, 1)
end
function outputlength(kernel::FIRArbitrary, inputlength::Integer)
ceil(Int, (inputlength-kernel.inputDeficit+1) * kernel.rate)
end
function outputlength(self::FIRFilter, inputlength::Integer)
outputlength(self.kernel, inputlength)
end
#
# Calculates the input length of a multirate filtering operation,
# given the output length
#
function inputlength(outputlength::Int, ratio::Rational, initialϕ::Integer)
interpolation = numerator(ratio)
decimation = denominator(ratio)
inLen = (outputlength * decimation + initialϕ - 1) / interpolation
floor(Int, inLen)
end
function inputlength(kernel::FIRStandard, outputlength::Integer)
outputlength
end
function inputlength(kernel::FIRInterpolator, outputlength::Integer)
inLen = inputlength(outputlength, kernel.interpolation//1, kernel.ϕIdx)
inLen += kernel.inputDeficit - 1
end
function inputlength(kernel::FIRDecimator, outputlength::Integer)
inLen = inputlength(outputlength, 1//kernel.decimation, 1)
inLen += kernel.inputDeficit - 1
end
function inputlength(kernel::FIRRational, outputlength::Integer)
inLen = inputlength(outputlength, kernel.ratio, kernel.ϕIdx)
inLen += kernel.inputDeficit - 1
end
# TODO: figure out why this fails. Might be fine, but the filter operation might not being stepping through the phases correcty.
function inputlength(kernel::FIRArbitrary, outputlength::Integer)
inLen = floor(Int, outputlength/kernel.rate)
inLen += kernel.inputDeficit - 1
end
function inputlength(self::FIRFilter, outputlength::Integer)
inputlength(self.kernel, outputlength)
end
#
# Calculates the delay caused by the FIR filter in # samples, at the input sample rate, caused by the filter process
#
function timedelay(kernel::Union{FIRRational, FIRInterpolator, FIRArbitrary})
(kernel.hLen - 1)/(2.0*kernel.Nϕ)
end
function timedelay(kernel::Union{FIRStandard, FIRDecimator})
(kernel.hLen - 1)/2
end
function timedelay(self::FIRFilter)
timedelay(self.kernel)
end
#
# Single rate filtering
#
function filt!(buffer::AbstractVector{Tb}, self::FIRFilter{FIRStandard{Th}}, x::AbstractVector{Tx}) where {Tb,Th,Tx}
kernel = self.kernel
history::Vector{Tx} = self.history
bufLen = length(buffer)
xLen = length(x)
bufLen >= xLen || error("buffer length must be >= x length")
h = kernel.h
for i = 1:min(kernel.hLen-1, xLen)
@inbounds buffer[i] = unsafe_dot(h, history, x, i)
end
for i = kernel.hLen:xLen
@inbounds buffer[i] = unsafe_dot(h, x, i)
end
self.history = shiftin!(history, x)
return xLen
end
function filt(self::FIRFilter{FIRStandard{Th}}, x::AbstractVector{Tx}) where {Th,Tx}
bufLen = outputlength(self, length(x))
buffer = Vector{promote_type(Th,Tx)}(undef, bufLen)
samplesWritten = filt!(buffer, self, x)
samplesWritten == bufLen || resize!(buffer, samplesWritten)
return buffer
end
#
# Interpolation
#
function filt!(buffer::AbstractVector{Tb}, self::FIRFilter{FIRInterpolator{Th}}, x::AbstractVector{Tx}) where {Tb,Th,Tx}
kernel = self.kernel
history::Vector{Tx} = self.history
interpolation = kernel.interpolation
xLen = length(x)
bufLen = length(buffer)
bufIdx = 0
if xLen < kernel.inputDeficit
self.history = shiftin!(history, x)
kernel.inputDeficit -= xLen
return bufIdx
end
inputIdx = kernel.inputDeficit
bufLen >= outputlength(self, xLen) || error("length(buffer) must be >= interpolation * length(x)")
while inputIdx <= xLen
bufIdx += 1
if inputIdx < kernel.tapsPerϕ
accumulator = unsafe_dot(kernel.pfb, kernel.ϕIdx, history, x, inputIdx)
else
accumulator = unsafe_dot(kernel.pfb, kernel.ϕIdx, x, inputIdx)
end
buffer[bufIdx] = accumulator
(kernel.ϕIdx, inputIdx) = kernel.ϕIdx == kernel.Nϕ ? (1, inputIdx+1) : (kernel.ϕIdx+1, inputIdx)
end
kernel.inputDeficit = 1
self.history = shiftin!(history, x)
return bufIdx
end
function filt(self::FIRFilter{FIRInterpolator{Th}}, x::AbstractVector{Tx}) where {Th,Tx}
bufLen = outputlength(self, length(x))
buffer = Vector{promote_type(Th,Tx)}(undef, bufLen)
samplesWritten = filt!(buffer, self, x)
samplesWritten == bufLen || resize!(buffer, samplesWritten)
return buffer
end
#
# Rational resampling
#
function filt!(buffer::AbstractVector{Tb}, self::FIRFilter{FIRRational{Th}}, x::AbstractVector{Tx}) where {Tb,Th,Tx}
kernel = self.kernel
history::Vector{Tx} = self.history
xLen = length(x)
bufLen = length(buffer)
bufIdx = 0
if xLen < kernel.inputDeficit
self.history = shiftin!(history, x)
kernel.inputDeficit -= xLen
return bufIdx
end
outLen = outputlength(xLen-kernel.inputDeficit+1, kernel.ratio, kernel.ϕIdx)
bufLen >= outLen || error("buffer is too small")
interpolation = numerator(kernel.ratio)
decimation = denominator(kernel.ratio)
inputIdx = kernel.inputDeficit
while inputIdx <= xLen
bufIdx += 1
if inputIdx < kernel.tapsPerϕ
accumulator = unsafe_dot(kernel.pfb, kernel.ϕIdx, history, x, inputIdx)
else
accumulator = unsafe_dot(kernel.pfb, kernel.ϕIdx, x, inputIdx)
end
buffer[bufIdx] = accumulator
inputIdx += div(kernel.ϕIdx + decimation - 1, interpolation)
ϕIdx = kernel.ϕIdx + kernel.ϕIdxStepSize
kernel.ϕIdx = ϕIdx > interpolation ? ϕIdx - interpolation : ϕIdx
end
kernel.inputDeficit = inputIdx - xLen
self.history = shiftin!(history, x)
return bufIdx
end
function filt(self::FIRFilter{FIRRational{Th}}, x::AbstractVector{Tx}) where {Th,Tx}
bufLen = outputlength(self, length(x))
buffer = Vector{promote_type(Th,Tx)}(undef, bufLen)
samplesWritten = filt!(buffer, self, x)
samplesWritten == bufLen || resize!(buffer, samplesWritten)
return buffer
end
#
# Decimation
#
function filt!(buffer::AbstractVector{Tb}, self::FIRFilter{FIRDecimator{Th}}, x::AbstractVector{Tx}) where {Tb,Th,Tx}
kernel = self.kernel
xLen = length(x)
history::Vector{Tx} = self.history
bufIdx = 0
if xLen < kernel.inputDeficit
self.history = shiftin!(history, x)
kernel.inputDeficit -= xLen
return bufIdx
end
outLen = outputlength(self, xLen)
inputIdx = kernel.inputDeficit
while inputIdx <= xLen
bufIdx += 1
if inputIdx < kernel.hLen
accumulator = unsafe_dot(kernel.h, history, x, inputIdx)
else
accumulator = unsafe_dot(kernel.h, x, inputIdx)
end
@inbounds buffer[bufIdx] = accumulator
inputIdx += kernel.decimation
end
kernel.inputDeficit = inputIdx - xLen
self.history = shiftin!(history, x)
return bufIdx
end
function filt(self::FIRFilter{FIRDecimator{Th}}, x::AbstractVector{Tx}) where {Th,Tx}
bufLen = outputlength(self, length(x))
buffer = Vector{promote_type(Th,Tx)}(undef, bufLen)
samplesWritten = filt!(buffer, self, x)
samplesWritten == bufLen || resize!(buffer, samplesWritten)
return buffer
end
#
# Arbitrary resampling
#
# Updates FIRArbitrary state. See Section 7.5.1 in [1].
# [1] uses a phase accumilator that increments by Δ (Nϕ/rate)
function update(kernel::FIRArbitrary)
kernel.ϕAccumulator += kernel.Δ
if kernel.ϕAccumulator > kernel.Nϕ
kernel.xIdx += div(kernel.ϕAccumulator-1, kernel.Nϕ)
kernel.ϕAccumulator = mod(kernel.ϕAccumulator-1, kernel.Nϕ) + 1
end
kernel.ϕIdx = floor(Int, kernel.ϕAccumulator)
kernel.α = kernel.ϕAccumulator - kernel.ϕIdx
end
function filt!(buffer::AbstractVector{Tb}, self::FIRFilter{FIRArbitrary{Th}}, x::AbstractVector{Tx}) where {Tb,Th,Tx}
kernel = self.kernel
pfb = kernel.pfb
dpfb = kernel.dpfb
xLen = length(x)
bufIdx = 0
history::Vector{Tx} = self.history
# Do we have enough input samples to produce one or more output samples?
if xLen < kernel.inputDeficit
self.history = shiftin!(history, x)
kernel.inputDeficit -= xLen
return bufIdx
end
# Skip over input samples that are not needed to produce output results.
# We do this by seting inputIdx to inputDeficit which was calculated in the previous run.
# InputDeficit is set to 1 when instantiation the FIRArbitrary kernel, that way the first
# input always produces an output.
kernel.xIdx = kernel.inputDeficit
while kernel.xIdx <= xLen
bufIdx += 1
if kernel.xIdx < kernel.tapsPerϕ
yLower = unsafe_dot(pfb, kernel.ϕIdx, history, x, kernel.xIdx)
yUpper = unsafe_dot(dpfb, kernel.ϕIdx, history, x, kernel.xIdx)
else
yLower = unsafe_dot(pfb, kernel.ϕIdx, x, kernel.xIdx)
yUpper = unsafe_dot(dpfb, kernel.ϕIdx, x, kernel.xIdx)
end
@inbounds buffer[bufIdx] = yLower + yUpper * kernel.α
update(kernel)
end
kernel.inputDeficit = kernel.xIdx - xLen
self.history = shiftin!(history, x)
return bufIdx
end
function filt(self::FIRFilter{FIRArbitrary{Th}}, x::AbstractVector{Tx}) where {Th,Tx}
bufLen = outputlength(self, length(x))
buffer = Vector{promote_type(Th,Tx)}(undef, bufLen)
samplesWritten = filt!(buffer, self, x)
samplesWritten == bufLen || resize!(buffer, samplesWritten)
return buffer
end
#
# Stateless filt implementations
#
# Single-rate, decimation, interpolation, and rational resampling.
function filt(h::Vector, x::AbstractVector, ratio::Rational)
self = FIRFilter(h, ratio)
filt(self, x)
end
# Arbitrary resampling with polyphase interpolation and two neighbor linear interpolation.
function filt(h::Vector, x::AbstractVector, rate::AbstractFloat, Nϕ::Integer=32)
self = FIRFilter(h, rate, Nϕ)
filt(self, x)
end
"""
resample(x, rate[, coef])
Resample `x` at rational or arbitrary `rate`.
`coef` is an optional vector of FIR filter taps. If `coef`
is not provided, the taps will be computed using a Kaiser window.
Internally, `resample` uses a polyphase `FIRFilter` object,
but performs additional operations to make resampling a signal easier.
It compensates for for the `FIRFilter`'s delay (ramp-up), and appends
zeros to `x`. The result is that when the input and output signals
are plotted on top of each other, they correlate very well, but one
signal will have more samples that the other.
"""
function resample(x::AbstractVector, rate::Real, h::Vector)
self = FIRFilter(h, rate)
# Get delay, in # of samples at the output rate, caused by filtering processes
τ = timedelay(self)
# Use setphase! to
# a) adjust the input samples to skip over before producing and output (integer part of τ)
# b) set the ϕ index of the PFB (fractional part of τ)
setphase!(self, τ)
# Calculate the number of 0's required
outLen = ceil(Int, length(x)*rate)
reqInlen = inputlength(self, outLen)
reqZerosLen = reqInlen - length(x)
xPadded = [x; zeros(eltype(x), reqZerosLen)]
filt(self, xPadded)
end
function resample(x::AbstractVector, rate::Real)
h = resample_filter(rate)
resample(x, rate, h)
end
#
# References
#
# [1] F.J. Harris, *Multirate Signal Processing for Communication Systems*. Prentice Hall, 2004
# [2] Dick, C.; Harris, F., "Options for arbitrary resamplers in FPGA-based modulators," Signals, Systems and Computers, 2004. Conference Record of the Thirty-Eighth Asilomar Conference on , vol.1, no., pp.777,781 Vol.1, 7-10 Nov. 2004
# [3] Kim, S.C.; Plishker, W.L.; Bhattacharyya, S.S., "An efficient GPU implementation of an arbitrary resampling polyphase channelizer," Design and Architectures for Signal and Image Processing (DASIP), 2013 Conference on, vol., no., pp.231,238, 8-10 Oct. 2013
# [4] Horridge, J.P.; Frazer, Gordon J., "Accurate arbitrary resampling with exact delay for radar applications," Radar, 2008 International Conference on , vol., no., pp.123,127, 2-5 Sept. 2008
# [5] Blok, M., "Fractional delay filter design for sample rate conversion," Computer Science and Information Systems (FedCSIS), 2012 Federated Conference on , vol., no., pp.701,706, 9-12 Sept. 2012