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Merge pull request #222 from matthuszagh/lockin

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Lockin
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Robert Jördens 2021-01-13 18:47:37 +01:00 committed by GitHub
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6 changed files with 114 additions and 1660 deletions
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21
dsp/src/lib.rs
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@ -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 +20,23 @@ 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. `dividend`+`divisor`-1 must be inside [i64::MIN,
/// i64::MAX].
///
/// # Returns
///
/// Divided and rounded value.
#[inline(always)]
pub fn divide_round(dividend: i64, divisor: i64) -> i64 {
(dividend + (divisor - 1)) / divisor
}
fn abs<T>(x: T) -> T
where
T: PartialOrd + Default + Neg<Output = T>,
@ -99,8 +116,8 @@ where
pub mod iir;
pub mod iir_int;
pub mod lockin;
pub mod pll;
pub mod reciprocal_pll;
pub mod trig;
pub mod unwrap;

518
dsp/src/lockin.rs
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@ -1,518 +0,0 @@
//! Lock-in amplifier.
//!
//! Lock-in processing is performed through a combination of the
//! following modular processing blocks: demodulation, filtering,
//! decimation and computing the magnitude and phase from a complex
//! signal. These processing blocks are mutually independent.
//!
//! # Terminology
//!
//! * _demodulation signal_ - A copy of the reference signal that is
//! optionally frequency scaled and phase shifted. This is a complex
//! signal. The demodulation signals are used to demodulate the ADC
//! sampled signal.
//! * _internal clock_ - A fast internal clock used to increment a
//! counter for determining the 0-phase points of a reference signal.
//! * _reference signal_ - A constant-frequency signal used to derive
//! the demodulation signal.
//! * _timestamp_ - Timestamps record the timing of the reference
//! signal's 0-phase points. For instance, if a reference signal is
//! provided externally, a fast internal clock increments a
//! counter. When the external reference reaches the 0-phase point
//! (e.g., a positive edge), the value of the counter is recorded as a
//! timestamp. These timestamps are used to determine the frequency
//! and phase of the reference signal.
//!
//! # Usage
//!
//! The first step is to initialize a `Lockin` instance with
//! `Lockin::new()`. This provides the lock-in algorithms with
//! necessary information about the demodulation and filtering steps,
//! such as whether to demodulate with a harmonic of the reference
//! signal and the IIR biquad filter to use. There are then 4
//! different processing steps that can be used:
//!
//! * `demodulate` - Computes the phase of the demodulation signal
//! corresponding to each ADC sample, uses this phase to compute the
//! demodulation signal, and multiplies this demodulation signal by
//! the ADC-sampled signal. This is a method of `Lockin` since it
//! requires information about how to modify the reference signal for
//! demodulation.
//! * `filter` - Performs IIR biquad filtering of a complex
//! signals. This is commonly performed on the signal provided by the
//! demodulation step, but can be performed at any other point in the
//! processing chain or omitted entirely. `filter` is a method of
//! `Lockin` since it must hold onto the filter configuration and
//! state.
//! * `decimate` - This decimates a signal to reduce the load on the
//! DAC output. It does not require any state information and is
//! therefore a normal function.
//! * `magnitude_phase` - Computes the magnitude and phase of the
//! component of the ADC-sampled signal whose frequency is equal to
//! 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;
/// 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],
iir: IIR,
iirstate: [IIRState; 2],
}
impl Lockin {
/// Initialize a new `Lockin` instance.
///
/// # 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.
/// * `iir` - IIR biquad filter.
///
/// # Returns
///
/// New `Lockin` instance.
pub fn new(
phase_offset: f32,
sample_period: u32,
harmonic: u32,
iir: IIR,
) -> Self {
Lockin {
phase_offset: phase_offset,
sample_period: sample_period,
harmonic: harmonic,
timestamps: [None, None],
iir: iir,
iirstate: [[0.; 5]; 2],
}
}
/// Demodulate an input signal with the complex reference signal.
///
/// # 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.
///
/// # 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 => (),
});
// 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 {
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 };
// compute ADC sample phases, sines/cosines and demodulate
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;
});
// record new timestamps
let start_index: usize = if timestamps.len() < 2 {
0
} else {
timestamps.len() - 2
};
timestamps[start_index..]
.iter()
.for_each(|t| self.timestamps.push(Some(*t as i32)));
Ok(signal)
}
/// Filter the complex signal using the supplied biquad IIR. The
/// signal array is modified in place.
///
/// # Arguments
///
/// * `signal` - Complex signal to filter.
pub fn filter(&mut self, signal: &mut [Complex<f32>]) {
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);
});
}
}
/// 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.
///
/// # Arguments
///
/// * `signal` - Complex signal to decimate.
///
/// # Returns
///
/// 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
);
let mut signal_decimated = [(0_f32, 0_f32); DECIMATED_BUFFER_SIZE];
signal_decimated
.iter_mut()
.zip(signal.iter().step_by(n_k))
.for_each(|(s_d, s)| {
s_d.0 = s.0;
s_d.1 = s.1;
});
signal_decimated
}
/// Compute the magnitude and phase from the complex signal. The
/// signal array is modified in place.
///
/// # Arguments
///
/// * `signal` - Complex signal to decimate.
pub fn magnitude_phase(signal: &mut [Complex<f32>]) {
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);
s.0 = new_i;
s.1 = new_q;
});
}
#[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() {
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], &[]),
Err("insufficient timestamps")
);
}
#[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")
);
}
#[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
);
}
}

92
dsp/src/reciprocal_pll.rs Normal file
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@ -0,0 +1,92 @@
use super::{divide_round, pll::PLL};
/// Processes external timestamps to produce the frequency and initial phase of the demodulation
/// signal.
pub struct TimestampHandler {
pll: PLL,
pll_shift_frequency: u8,
pll_shift_phase: u8,
// Index of the current ADC batch.
batch_index: u32,
// Most recent phase and frequency values of the external reference.
reference_phase: i64,
reference_frequency: i64,
adc_sample_ticks_log2: usize,
sample_buffer_size_log2: usize,
}
impl TimestampHandler {
/// Construct a new `TimestampHandler` instance.
///
/// # Args
/// * `pll_shift_frequency` - See `PLL::update()`.
/// * `pll_shift_phase` - See `PLL::update()`.
/// * `adc_sample_ticks_log2` - Number of ticks in one ADC sampling timer period.
/// * `sample_buffer_size_log2` - Number of ADC samples in one processing batch.
///
/// # Returns
/// New `TimestampHandler` instance.
pub fn new(
pll_shift_frequency: u8,
pll_shift_phase: u8,
adc_sample_ticks_log2: usize,
sample_buffer_size_log2: usize,
) -> Self {
TimestampHandler {
pll: PLL::default(),
pll_shift_frequency,
pll_shift_phase,
batch_index: 0,
reference_phase: 0,
reference_frequency: 0,
adc_sample_ticks_log2,
sample_buffer_size_log2,
}
}
/// Compute the initial phase and frequency of the demodulation signal.
///
/// # Args
/// * `timestamp` - Counter value corresponding to an external reference edge.
///
/// # Returns
/// Tuple consisting of the initial phase value and frequency of the demodulation signal.
pub fn update(&mut self, timestamp: Option<u32>) -> (u32, u32) {
if let Some(t) = timestamp {
let (phase, frequency) = self.pll.update(
t as i32,
self.pll_shift_frequency,
self.pll_shift_phase,
);
self.reference_phase = phase as u32 as i64;
self.reference_frequency = frequency as u32 as i64;
}
let demodulation_frequency = divide_round(
1 << (32 + self.adc_sample_ticks_log2),
self.reference_frequency,
) as u32;
let demodulation_initial_phase = divide_round(
(((self.batch_index as i64)
<< (self.adc_sample_ticks_log2
+ self.sample_buffer_size_log2))
- self.reference_phase)
<< 32,
self.reference_frequency,
) as u32;
if self.batch_index
< (1 << (32
- self.adc_sample_ticks_log2
- self.sample_buffer_size_log2))
- 1
{
self.batch_index += 1;
} else {
self.batch_index = 0;
self.reference_phase -= 1 << 32;
}
(demodulation_initial_phase, demodulation_frequency)
}
}

1137
dsp/tests/lockin_low_pass.rs
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File diff suppressed because it is too large Load Diff

4
src/digital_input_stamper.rs
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@ -26,13 +26,13 @@
///! timestamping is desired in DI1, a separate timer + capture channel will be necessary.
use super::{hal, timers, ADC_SAMPLE_TICKS, SAMPLE_BUFFER_SIZE};
/// Calculate the period of the digital input timestampe timer.
/// Calculate the period of the digital input timestamp timer.
///
/// # Note
/// The period returned will be 1 less than the required period in timer ticks. The value returned
/// can be immediately programmed into a hardware timer period register.
///
/// The period is calcualted to be some power-of-two multiple of the batch size, such that N batches
/// The period is calculated to be some power-of-two multiple of the batch size, such that N batches
/// will occur between each timestamp timer overflow.
///
/// # Returns

2
src/main.rs
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@ -353,7 +353,7 @@ const APP: () = {
timer5.pause();
timer5.set_tick_freq(design_parameters::TIMER_FREQUENCY);
// The time stamp timer must run at exactly a multiple of the sample timer based on the
// The timestamp timer must run at exactly a multiple of the sample timer based on the
// batch size. To accomodate this, we manually set the prescaler identical to the sample
// timer, but use a period that is longer.
let mut timer = timers::TimestampTimer::new(timer5);