Impulse will be a collection of signal processing primitives for Nim.
The FFT part of this library wraps PocketFFT.
For the C++ backend an optimized version of PocketFFT is used, in the form of a header-only version,
https://github.com/mreineck/pocketfft
For the C backend we use the PocketFFT directly (the C library linked before).
Note that the API differs slightly between the two. See the two examples below.
The pocketfft submodule can to be imported manually using
import impulse/fft/pocketfft or one can simply import the fft
submodule as shown below.
import impulse/fft
template isClose(a1, a2, eps: untyped): untyped =
for i in 0 ..< a1.len:
doAssert abs(a1[i] - a2[i]) < eps, "Is: " & $a1[i] & " | " & $a2[i]
block Array:
let dIn = [1.0, 2.0, 1.0, -1.0, 1.5]
let dOut = fft(dIn, forward = true) # forward or backwards?
echo dIn
echo dOut
isClose(dIn, fft(dOut, forward = false), eps = 1e-10)
# [1.0, 2.0, 1.0, -1.0, 1.5]
# @[4.5, 2.081559480312316, -1.651098762732523, -1.831559480312316, 1.608220406444071]
block Seq:
let dIn = @[1.0, 2.0, 1.0, -1.0, 1.5]
let dOut = fft(dIn, forward = true) # forward or backwards?
echo dIn
echo dOut
isClose(dIn, fft(dOut, forward = false), eps = 1e-10)
# @[1.0, 2.0, 1.0, -1.0, 1.5]
# @[4.5, 2.081559480312316, -1.651098762732523, -1.831559480312316, 1.608220406444071]
block Tensor:
let dIn = @[1.0, 2.0, 1.0, -1.0, 1.5].toTensor
let dOut = fft(dIn, forward = true) # forward or backwards?
echo dIn
echo dOut
isClose(dIn, fft(dOut, forward = false), eps = 1e-10)
# Tensor[system.float] of shape "[5]" on backend "Cpu"
# 1 2 1 -1 1.5
# Tensor[system.float] of shape "[5]" on backend "Cpu"
# 4.5 2.08156 -1.6511 -1.83156 1.60822
import std / complex
block Complex:
let dIn = [complex(1.0), complex(2.0), complex(1.0), complex(-1.0), complex(1.5)]
let dOut = fft(dIn, forward = true) # forward or backwards?
echo dIn
echo dOut
isClose(dIn, fft(dOut, forward = false), eps = 1e-10)
# [(1.0, 0.0), (2.0, 0.0), (1.0, 0.0), (-1.0, 0.0), (1.5, 0.0)]
# @[(4.5, 0.0), (2.081559480312316, -1.651098762732523), (-1.831559480312316, 1.608220406444071), (-1.831559480312316, -1.608220406444071), (2.081559480312316, 1.651098762732523)]When compiling on the C++ backend, the API is a bit different:
import impulse/fft
import std / complex
let dIn = @[1.0, 2.0, 1.0, -1.0, 1.5]
var dOut = newSeq[Complex[float64]](dIn.len)
let dInDesc = DataDesc[float64].init(
dIn[0].unsafeAddr, [dIn.len]
)
var dOutDesc = DataDesc[Complex[float64]].init(
dOut[0].addr, [dOut.len]
)
let fft = FFTDesc[float64].init(
axes = [0],
forward = true
)
fft.apply(dOutDesc, dInDesc)
echo dIn
echo dOut
# @[1.0, 2.0, 1.0, -1.0, 1.5]
# @[(4.5, 0.0), (2.081559480312316, -1.651098762732523), (-1.831559480312316, 1.608220406444071), (0.0, 0.0), (0.0, 0.0)]LFSR module which implements a Linear Feedback Shift Register that can be used to generate pseudo-random boolean sequences. It supports both Fibonacci and Galois LFSRs.
LFSRs used in many digital communication systems (including, for example LTE and 5GNR). For more information see:
https://simple.wikipedia.org/wiki/Linear-feedback_shift_register
Note that this module uses Arraymancer under the hood, so it depends on it. Also note that this code is heavily based on Nikesh Bajaj's pylfsr, which can be found in https://pylfsr.github.io
The following example creates a Fibonacci-style LFSR with polynomial
x^5 + x^3 + 1 and uses it to generate a pseudo-random sequence of 31 values.
Note how the taps argument is an integer tensor with values [5, 3],
corresponding to the exponents of the coefficients of the polynomial, in
descending order. Exponent 0 was skipped because it is implicitly included
(if it is included it will be ignored). If the exponents are not in
descending order a ValueError exception will be raised.
import impulse/lfsr
import arraymancer
var fibonacci_lfsr = initLFSR(
taps = [5, 3], # descending order and 0 can be omitted
# The following 2 lines can be skipped in this case since they are the defaults
# state = single_true,
# conf = fibonacci
)
let sequence1 = fibonacci_lfsr.generate(31)
# Print the first few elements
# Note that sequence1 will be a Tensor[bool] but it can be easily converted to
# Tensor[int] for more concise printing
echo sequence1.asType(int)[_..11]
# Tensor[system.int] of shape "[12]" on backend "Cpu"
# 1 0 0 0 0 1 0 0 1 0 1 1
# The generator can be reset to start over
fibonacci_lfsr.reset()
let sequence2 = fibonacci_lfsr.generate(31)
doAssert sequence1 == sequence2Galois style LFSRs are also supported and it is also possible to set a custom start state as a Tensor[bool]:
var galois_lfsr = initLFSR(
# note how the 0 exponent can be included and taps can be a Tensor as well
taps = [5, 3, 0].toTensor,
state = [true, true, true, true, true].toTensor, # this is equivalent to `all_true`
conf = galois
)
# Generate the first 8 values
let sequence3a = galois_lfsr.generate(8)
echo sequence3a.asType(int)
# Tensor[system.int] of shape "[8]" on backend "Cpu"
# 1 1 1 1 0 0 0 1
# Generate a few more values
let sequence3b = galois_lfsr.generate(10)
echo sequence3b.asType(int)
# Tensor[system.int] of shape "[10]" on backend "Cpu"
# 1 0 1 1 1 0 1 0 1 0
galois_lfsr.reset()
echo galois_lfsr.generate(18)
# Tensor[system.int] of shape "[18]" on backend "Cpu"
# 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0As a convenience, a tap_examples function is provided. This function takes a
size and returns one example (out of many) sequence of taps that generates a
"maximal" LSFR sequence.
The LFSR module implementation is favors simplicity over speed. As of 2024, it is able to generate 2^24 values in less than 1 minute on a mid-range laptop.
The Signal module implements several signal processing and related functions, such as a Kaiser window and a firls FIR filter design function. See the documentation of those functions for more details.
Licensed and distributed under either of
- MIT license: LICENSE-MIT or http://opensource.org/licenses/MIT
or
- Apache License, Version 2.0, (LICENSE-APACHEv2 or http://www.apache.org/licenses/LICENSE-2.0)
at your option. These files may not be copied, modified, or distributed except according to those terms.