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update lock-in for integer math and PLL

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This commit is contained in:
Matt Huszagh 2021-01-08 11:53:08 -08:00
parent 028f4a1bb2
commit bae295140d
3 changed files with 238 additions and 1483 deletions
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21
dsp/src/lib.rs
View File

@ -5,7 +5,7 @@ use core::ops::{Add, Mul, Neg};
pub type Complex<T> = (T, T);
/// Round up half.
/// Bit shift, round up half.
///
/// # Arguments
///
@ -20,6 +20,25 @@ pub fn shift_round(x: i32, shift: usize) -> i32 {
(x + (1 << (shift - 1))) >> shift
}
/// Integer division, round up half.
///
/// # Arguments
///
/// `dividend` - Value to divide.
/// `divisor` - Value that divides the dividend.
///
/// # Returns
///
/// Divided and rounded value.
#[inline(always)]
pub fn divide_round(dividend: i64, divisor: i64) -> i64 {
debug_assert!(
dividend as i128 + (divisor as i128 - 1) < i64::MAX as i128
&& dividend as i128 + (divisor as i128 - 1) > i64::MIN as i128
);
(dividend + (divisor - 1)) / divisor
}
fn abs<T>(x: T) -> T
where
T: PartialOrd + Default + Neg<Output = T>,

559
dsp/src/lockin.rs
View File

@ -52,47 +52,36 @@
//! the demodulation frequency. This does not require any state
//! information and is therefore a normal function.
use super::iir::{IIRState, IIR};
use super::Complex;
use core::f32::consts::PI;
use super::iir_int::{IIRState, IIR};
use super::pll::PLL;
use super::trig::{atan2, cossin};
use super::{divide_round, Complex};
/// TODO these constants are copied from main.rs and should be
/// shared. Additionally, we should probably store the log2 values and
/// compute the actual values from these in main, as is done here.
pub const SAMPLE_BUFFER_SIZE_LOG2: usize = 0;
pub const SAMPLE_BUFFER_SIZE: usize = 1 << SAMPLE_BUFFER_SIZE_LOG2;
pub const ADC_SAMPLE_TICKS_LOG2: usize = 8;
pub const ADC_SAMPLE_TICKS: usize = 1 << ADC_SAMPLE_TICKS_LOG2;
pub const ADC_BATCHES_LOG2: usize =
32 - SAMPLE_BUFFER_SIZE_LOG2 - ADC_SAMPLE_TICKS_LOG2;
pub const ADC_BATCHES: usize = 1 << ADC_BATCHES_LOG2;
/// The number of ADC samples in one batch.
pub const ADC_SAMPLE_BUFFER_SIZE: usize = 16;
/// The number of outputs sent to the DAC for each ADC batch.
pub const DECIMATED_BUFFER_SIZE: usize = 1;
/// Treat the 2-element array as a FIFO. This allows new elements to
/// be pushed into the array, existing elements to shift back in the
/// array, and the last element to fall off the array.
trait Fifo2<T> {
fn push(&mut self, new_element: Option<T>);
}
impl<T: Copy> Fifo2<T> for [Option<T>; 2] {
/// Push a new element into the array. The existing elements move
/// backward in the array by one location, and the current last
/// element is discarded.
///
/// # Arguments
///
/// * `new_element` - New element pushed into the front of the
/// array.
fn push(&mut self, new_element: Option<T>) {
// For array sizes greater than 2 it would be preferable to
// use a rotating index to avoid unnecessary data
// copying. However, this would somewhat complicate the use of
// iterators and for 2 elements, shifting is inexpensive.
self[1] = self[0];
self[0] = new_element;
}
}
/// Performs lock-in amplifier processing of a signal.
pub struct Lockin {
phase_offset: f32,
sample_period: u32,
harmonic: u32,
timestamps: [Option<i32>; 2],
phase_offset: u32,
batch_index: u32,
last_phase: Option<i64>,
last_frequency: Option<i64>,
pll: PLL,
pll_shift_frequency: u8,
pll_shift_phase: u8,
iir: IIR,
iirstate: [IIRState; 2],
}
@ -102,31 +91,36 @@ impl Lockin {
///
/// # Arguments
///
/// * `phase_offset` - Phase offset (in radians) applied to the
/// demodulation signal.
/// * `sample_period` - ADC sampling period in terms of the
/// internal clock period.
/// * `harmonic` - Integer scaling factor used to adjust the
/// demodulation frequency. E.g., 2 would demodulate with the
/// first harmonic.
/// * `phase_offset` - Phase offset applied to the demodulation
/// signal.
/// * `iir` - IIR biquad filter.
/// * `pll_shift_frequency` - See PLL::update().
/// * `pll_shift_phase` - See PLL::update().
///
/// # Returns
///
/// New `Lockin` instance.
pub fn new(
phase_offset: f32,
sample_period: u32,
harmonic: u32,
phase_offset: u32,
iir: IIR,
pll_shift_frequency: u8,
pll_shift_phase: u8,
) -> Self {
Lockin {
phase_offset: phase_offset,
sample_period: sample_period,
harmonic: harmonic,
timestamps: [None, None],
iir: iir,
iirstate: [[0.; 5]; 2],
harmonic,
phase_offset,
batch_index: 0,
last_phase: None,
last_frequency: None,
pll: PLL::default(),
pll_shift_frequency,
pll_shift_phase,
iir,
iirstate: [[0; 5]; 2],
}
}
@ -135,120 +129,88 @@ impl Lockin {
/// # Arguments
///
/// * `adc_samples` - One batch of ADC samples.
/// * `timestamps` - Counter values corresponding to the edges of
/// an external reference signal. The counter is incremented by a
/// fast internal clock.
/// * `timestamp` - Counter value corresponding to the edges of an
/// external reference signal. The counter is incremented by a
/// fast internal clock. Each ADC sample batch can contain 0 or 1
/// timestamps.
///
/// # Returns
///
/// The demodulated complex signal as a `Result`. When there are
/// an insufficient number of timestamps to perform processing,
/// `Err` is returned.
///
/// # Assumptions
///
/// `demodulate` expects that the timestamp counter value is equal
/// to 0 when the ADC samples its first input in a batch. This can
/// be achieved by configuring the timestamp counter to overflow
/// at the end of the ADC batch sampling period.
pub fn demodulate(
&mut self,
adc_samples: &[i16],
timestamps: &[u16],
) -> Result<[Complex<f32>; ADC_SAMPLE_BUFFER_SIZE], &str> {
let sample_period = self.sample_period as i32;
// update old timestamps for new ADC batch
self.timestamps.iter_mut().for_each(|t| match *t {
Some(timestamp) => {
// Existing timestamps have aged by one ADC batch
// period since the last ADC batch.
*t = Some(
timestamp - ADC_SAMPLE_BUFFER_SIZE as i32 * sample_period,
);
}
None => (),
});
timestamp: Option<u32>,
) -> Result<[Complex<i32>; SAMPLE_BUFFER_SIZE], &str> {
let frequency: i64;
let phase: i64;
// return prematurely if there aren't enough timestamps for
// processing
let old_timestamp_count =
self.timestamps.iter().filter(|t| t.is_some()).count();
if old_timestamp_count + timestamps.len() < 2 {
match timestamp {
Some(t) => {
let res = self.pll.update(
t as i32,
self.pll_shift_frequency,
self.pll_shift_phase,
);
phase = res.0 as u32 as i64;
frequency = res.1 as u32 as i64;
self.last_phase = Some(phase);
self.last_frequency = Some(frequency);
}
None => match self.last_phase {
Some(t) => {
phase = t;
frequency = self.last_frequency.unwrap();
}
None => {
self.batch_index += 1;
if self.batch_index == ADC_BATCHES as u32 {
self.batch_index = 0;
}
return Err("insufficient timestamps");
}
},
}
let mut signal = [(0., 0.); ADC_SAMPLE_BUFFER_SIZE];
// if we have not yet recorded any timestamps, the first
// reference period must be computed from the first and
// second timestamps in the array
let mut timestamp_index: usize =
if old_timestamp_count == 0 { 1 } else { 0 };
let demodulation_frequency = divide_round(
1 << (64 - SAMPLE_BUFFER_SIZE_LOG2 - ADC_BATCHES_LOG2),
frequency,
) as u32;
let demodulation_initial_phase = divide_round(
(((self.batch_index as i64) << (32 - ADC_BATCHES_LOG2)) - phase)
<< 32,
frequency,
) as u32;
// compute ADC sample phases, sines/cosines and demodulate
signal
let mut demodulation_signal = [(0_i32, 0_i32); SAMPLE_BUFFER_SIZE];
demodulation_signal
.iter_mut()
.zip(adc_samples.iter())
.enumerate()
.for_each(|(i, (s, sample))| {
let adc_sample_count = i as i32 * sample_period;
// index of the closest timestamp that occurred after
// the current ADC sample
let closest_timestamp_after_index: i32 = if timestamps.len() > 0
{
// Linear search is fast because both the timestamps
// and ADC sample counts are sorted. Because of this,
// we only need to check timestamps that were also
// greater than the last ADC sample count.
while timestamp_index < timestamps.len() - 1
&& (timestamps[timestamp_index] as i32)
< adc_sample_count
{
timestamp_index += 1;
}
timestamp_index as i32
} else {
-1
};
// closest timestamp that occurred before the current
// ADC sample
let closest_timestamp_before: i32;
let reference_period = if closest_timestamp_after_index < 0 {
closest_timestamp_before = self.timestamps[0].unwrap();
closest_timestamp_before - self.timestamps[1].unwrap()
} else if closest_timestamp_after_index == 0 {
closest_timestamp_before = self.timestamps[0].unwrap();
timestamps[0] as i32 - closest_timestamp_before
} else {
closest_timestamp_before = timestamps
[(closest_timestamp_after_index - 1) as usize]
as i32;
timestamps[closest_timestamp_after_index as usize] as i32
- closest_timestamp_before
};
let integer_phase: i32 = (adc_sample_count
- closest_timestamp_before)
* self.harmonic as i32;
let phase = self.phase_offset
+ 2. * PI * integer_phase as f32 / reference_period as f32;
let (sine, cosine) = libm::sincosf(phase);
let sample = *sample as f32;
s.0 = sine * sample;
s.1 = cosine * sample;
let sample_phase = (self.harmonic.wrapping_mul(
(demodulation_frequency.wrapping_mul(i as u32))
.wrapping_add(demodulation_initial_phase),
))
.wrapping_add(self.phase_offset);
let (cos, sin) = cossin(sample_phase as i32);
// cos/sin take up 32 bits and sample takes up 16
// bits. Make this fit into a 32 bit result.
s.0 = ((*sample as i64 * cos as i64) >> 16) as i32;
s.1 = ((*sample as i64 * sin as i64) >> 16) as i32;
});
// record new timestamps
let start_index: usize = if timestamps.len() < 2 {
0
if self.batch_index < ADC_BATCHES as u32 - 1 {
self.batch_index += 1;
} else {
timestamps.len() - 2
};
timestamps[start_index..]
.iter()
.for_each(|t| self.timestamps.push(Some(*t as i32)));
self.batch_index = 0;
self.last_phase = Some(self.last_phase.unwrap() - (1 << 32));
}
Ok(signal)
Ok(demodulation_signal)
}
/// Filter the complex signal using the supplied biquad IIR. The
@ -257,7 +219,7 @@ impl Lockin {
/// # Arguments
///
/// * `signal` - Complex signal to filter.
pub fn filter(&mut self, signal: &mut [Complex<f32>]) {
pub fn filter(&mut self, signal: &mut [Complex<i32>]) {
signal.iter_mut().for_each(|s| {
s.0 = self.iir.update(&mut self.iirstate[0], s.0);
s.1 = self.iir.update(&mut self.iirstate[1], s.1);
@ -266,8 +228,8 @@ impl Lockin {
}
/// Decimate the complex signal to `DECIMATED_BUFFER_SIZE`. The ratio
/// of `ADC_SAMPLE_BUFFER_SIZE` to `DECIMATED_BUFFER_SIZE` must be a
/// power of 2.
/// of `SAMPLE_BUFFER_SIZE` to `DECIMATED_BUFFER_SIZE` must be a power
/// of 2.
///
/// # Arguments
///
@ -277,14 +239,12 @@ impl Lockin {
///
/// The decimated signal.
pub fn decimate(
signal: [Complex<f32>; ADC_SAMPLE_BUFFER_SIZE],
) -> [Complex<f32>; DECIMATED_BUFFER_SIZE] {
let n_k = ADC_SAMPLE_BUFFER_SIZE / DECIMATED_BUFFER_SIZE;
debug_assert!(
ADC_SAMPLE_BUFFER_SIZE == DECIMATED_BUFFER_SIZE || n_k % 2 == 0
);
signal: [Complex<i32>; SAMPLE_BUFFER_SIZE],
) -> [Complex<i32>; DECIMATED_BUFFER_SIZE] {
let n_k = SAMPLE_BUFFER_SIZE / DECIMATED_BUFFER_SIZE;
debug_assert!(SAMPLE_BUFFER_SIZE == DECIMATED_BUFFER_SIZE || n_k % 2 == 0);
let mut signal_decimated = [(0_f32, 0_f32); DECIMATED_BUFFER_SIZE];
let mut signal_decimated = [(0_i32, 0_i32); DECIMATED_BUFFER_SIZE];
signal_decimated
.iter_mut()
@ -302,11 +262,13 @@ pub fn decimate(
///
/// # Arguments
///
/// * `signal` - Complex signal to decimate.
pub fn magnitude_phase(signal: &mut [Complex<f32>]) {
/// * `signal` - Complex signal for which the magnitude and phase
/// should be computed. TODO currently, we compute the square of the
/// magnitude. This should be changed to be the actual magnitude.
pub fn magnitude_phase(signal: &mut [Complex<i32>]) {
signal.iter_mut().for_each(|s| {
let new_i = libm::sqrtf([s.0, s.1].iter().map(|i| i * i).sum());
let new_q = libm::atan2f(s.1, s.0);
let new_i = [s.0, s.1].iter().map(|i| i * i).sum();
let new_q = atan2(s.1, s.0);
s.0 = new_i;
s.1 = new_q;
});
@ -315,204 +277,115 @@ pub fn magnitude_phase(signal: &mut [Complex<f32>]) {
#[cfg(test)]
mod tests {
use super::*;
use crate::testing::complex_allclose;
#[test]
fn array_push() {
let mut arr: [Option<u32>; 2] = [None, None];
arr.push(Some(1));
assert_eq!(arr, [Some(1), None]);
arr.push(Some(2));
assert_eq!(arr, [Some(2), Some(1)]);
arr.push(Some(10));
assert_eq!(arr, [Some(10), Some(2)]);
}
#[test]
fn magnitude_phase_length_1_quadrant_1() {
let mut signal: [Complex<f32>; 1] = [(1., 1.)];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(2_f32.sqrt(), PI / 4.)],
f32::EPSILON,
0.
));
signal = [(3_f32.sqrt() / 2., 1. / 2.)];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(1., PI / 6.)],
f32::EPSILON,
0.
));
}
#[test]
fn magnitude_phase_length_1_quadrant_2() {
let mut signal = [(-1., 1.)];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(2_f32.sqrt(), 3. * PI / 4.)],
f32::EPSILON,
0.
));
signal = [(-1. / 2., 3_f32.sqrt() / 2.)];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(1_f32, 2. * PI / 3.)],
f32::EPSILON,
0.
));
}
#[test]
fn magnitude_phase_length_1_quadrant_3() {
let mut signal = [(-1. / 2_f32.sqrt(), -1. / 2_f32.sqrt())];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(1_f32.sqrt(), -3. * PI / 4.)],
f32::EPSILON,
0.
));
signal = [(-1. / 2., -2_f32.sqrt())];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[((3. / 2.) as f32, -1.91063323625 as f32)],
f32::EPSILON,
0.
));
}
#[test]
fn magnitude_phase_length_1_quadrant_4() {
let mut signal = [(1. / 2_f32.sqrt(), -1. / 2_f32.sqrt())];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(1_f32.sqrt(), -1. * PI / 4.)],
f32::EPSILON,
0.
));
signal = [(3_f32.sqrt() / 2., -1. / 2.)];
magnitude_phase(&mut signal);
assert!(complex_allclose(
&signal,
&[(1_f32, -PI / 6.)],
f32::EPSILON,
0.
));
}
#[test]
fn decimate_sample_16_decimated_1() {
let signal: [Complex<f32>; ADC_SAMPLE_BUFFER_SIZE] = [
(0.0, 1.6),
(0.1, 1.7),
(0.2, 1.8),
(0.3, 1.9),
(0.4, 2.0),
(0.5, 2.1),
(0.6, 2.2),
(0.7, 2.3),
(0.8, 2.4),
(0.9, 2.5),
(1.0, 2.6),
(1.1, 2.7),
(1.2, 2.8),
(1.3, 2.9),
(1.4, 3.0),
(1.5, 3.1),
];
assert_eq!(decimate(signal), [(0.0, 1.6)]);
}
#[test]
fn lockin_demodulate_valid_0() {
/// Ensure that the demodulation signals are within some tolerance
/// band of the target value given the phase and frequency values
/// provided by the PLL.
fn demodulate() {
const PLL_SHIFT_FREQUENCY: u8 = 4;
const PLL_SHIFT_PHASE: u8 = 3;
const HARMONIC: u32 = 1;
const PHASE_OFFSET: u32 = 0;
let mut lockin = Lockin::new(
0.,
200,
1,
IIR {
ba: [0_f32; 5],
y_offset: 0.,
y_min: -(1 << 15) as f32,
y_max: (1 << 15) as f32 - 1.,
},
HARMONIC,
PHASE_OFFSET,
IIR { ba: [0; 5] },
PLL_SHIFT_FREQUENCY,
PLL_SHIFT_PHASE,
);
assert_eq!(
lockin.demodulate(&[0; ADC_SAMPLE_BUFFER_SIZE], &[]),
Err("insufficient timestamps")
// Duplicate the PLL outside demodulate so that we don't test
// its behavior.
let mut tracking_pll = PLL::default();
let mut tracking_phase: i32 = 0;
let mut tracking_frequency: i32 = 0;
const REFERENCE_FREQUENCY: usize = 10_000;
let mut reference_edge: usize = REFERENCE_FREQUENCY;
// Ensure that we receive at most 1 timestamp per batch.
debug_assert!(
REFERENCE_FREQUENCY >= SAMPLE_BUFFER_SIZE * ADC_SAMPLE_TICKS
);
for batch in 0..100_000 {
let tick: usize = batch * ADC_SAMPLE_TICKS * SAMPLE_BUFFER_SIZE;
let timestamp: Option<u32>;
// When the reference edge occurred during the current
// batch acquisition, register the timestamp and update
// the tracking PLL.
if reference_edge >= tick
&& reference_edge < tick + ADC_SAMPLE_TICKS * SAMPLE_BUFFER_SIZE
{
timestamp = Some(reference_edge as u32);
let tracking_update = tracking_pll.update(
reference_edge as i32,
PLL_SHIFT_FREQUENCY,
PLL_SHIFT_PHASE,
);
tracking_phase = tracking_update.0;
tracking_frequency = tracking_update.1;
reference_edge += REFERENCE_FREQUENCY;
} else {
timestamp = None;
}
#[test]
fn lockin_demodulate_valid_1() {
let mut lockin = Lockin::new(
0.,
200,
1,
IIR {
ba: [0_f32; 5],
y_offset: 0.,
y_min: -(1 << 15) as f32,
y_max: (1 << 15) as f32 - 1.,
},
);
assert_eq!(
lockin.demodulate(&[0; ADC_SAMPLE_BUFFER_SIZE], &[0],),
Err("insufficient timestamps")
);
}
let timestamp_before_batch = if tracking_phase > tick as i32 {
// There can be at most 1 reference edge per batch, so
// this will necessarily place the timestamp prior to
// the current batch.
tracking_phase - tracking_frequency
} else {
tracking_phase
};
#[test]
fn lockin_demodulate_valid_2() {
let adc_period: u32 = 200;
let mut lockin = Lockin::new(
0.,
adc_period,
1,
IIR {
ba: [0_f32; 5],
y_offset: 0.,
y_min: -(1 << 15) as f32,
y_max: (1 << 15) as f32 - 1.,
},
);
let adc_samples: [i16; ADC_SAMPLE_BUFFER_SIZE] =
[-8, 7, -7, 6, -6, 5, -5, 4, -4, 3, -3, 2, -2, -1, 1, 0];
let reference_period: u16 = 2800;
let initial_phase_integer: u16 = 200;
let timestamps: &[u16] = &[
initial_phase_integer,
initial_phase_integer + reference_period,
];
let initial_phase: f32 =
-(initial_phase_integer as f32) / reference_period as f32 * 2. * PI;
let phase_increment: f32 =
adc_period as f32 / reference_period as f32 * 2. * PI;
let mut signal = [(0., 0.); ADC_SAMPLE_BUFFER_SIZE];
for (n, s) in signal.iter_mut().enumerate() {
let adc_phase = initial_phase + n as f32 * phase_increment;
let sine = adc_phase.sin();
let cosine = adc_phase.cos();
s.0 = sine * adc_samples[n] as f32;
s.1 = cosine * adc_samples[n] as f32;
}
let result = lockin.demodulate(&adc_samples, timestamps).unwrap();
assert!(
complex_allclose(&result, &signal, 0., 1e-5),
"\nsignal computed: {:?},\nsignal expected: {:?}",
result,
signal
let initial_phase = (((tick as f64
- timestamp_before_batch as f64)
/ tracking_frequency as f64
* (1_i64 << 32) as f64)
.round()
% u32::MAX as f64) as u32;
let frequency = ((ADC_SAMPLE_TICKS as f64
/ tracking_frequency as f64
* (1_i64 << 32) as f64)
.round()
% u32::MAX as f64) as u32;
match lockin.demodulate(&[i16::MAX; SAMPLE_BUFFER_SIZE], timestamp)
{
Ok(v) => {
println!("batch : {}", batch);
for sample in 0..SAMPLE_BUFFER_SIZE {
const TOL: i32 = 50_000;
let cos = v[sample].0;
let sin = v[sample].1;
let (mut target_cos, mut target_sin) = cossin(
HARMONIC
.wrapping_mul(
(frequency.wrapping_mul(sample as u32))
.wrapping_add(initial_phase),
)
.wrapping_add(PHASE_OFFSET)
as i32,
);
target_cos /= 2;
target_sin /= 2;
println!("sample : {}", sample);
println!("tol : {}", TOL);
println!("cos, target: {}, {}", cos, target_cos);
println!("sin, target: {}, {}", sin, target_sin);
assert!((cos - target_cos).abs() < TOL);
assert!((sin - target_sin).abs() < TOL);
}
}
Err(_) => {}
}
}
}
}

1137
dsp/tests/lockin_low_pass.rs
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