dsp: replace in_phase and quadrature with Complex

dsp/src/complex.rs

@@ -0,0 +1,21 @@
+use core::cmp::PartialEq;
+
+#[derive(Copy, Clone, Debug, PartialEq)]
+pub struct Complex {
+    pub re: f32,
+    pub im: f32,
+}
+
+impl Complex {
+    pub fn new(re: f32, im: f32) -> Self {
+        Complex { re: re, im: im }
+    }
+
+    pub fn arg(&self) -> f32 {
+        libm::atan2f(self.im, self.re)
+    }
+
+    pub fn abs(&self) -> f32 {
+        libm::sqrtf([self.re, self.im].iter().map(|i| i * i).sum())
+    }
+}

dsp/src/lib.rs

@@ -1,6 +1,7 @@
 #![cfg_attr(not(test), no_std)]
 #![cfg_attr(feature = "nightly", feature(asm, core_intrinsics))]
 
+pub mod complex;
 pub mod iir;
 pub mod lockin;
 pub mod pll;

dsp/src/lockin.rs

@@ -2,25 +2,15 @@
 //!
 //! Lock-in processing is performed through a combination of the
 //! following modular processing blocks: demodulation, filtering,
-//! decimation and computing the magnitude and phase from the in-phase
+//! decimation and computing the magnitude and phase from a complex
-//! and quadrature signals. These processing blocks are mutually
+//! signal. These processing blocks are mutually independent.
-//! independent.
 //!
 //! # Terminology
 //!
 //! * _demodulation signal_ - A copy of the reference signal that is
-//! optionally frequency scaled and phase shifted. There are two
+//! optionally frequency scaled and phase shifted. This is a complex
-//! copies of this signal. The first copy is in-phase with the
+//! signal. The demodulation signals are used to demodulate the ADC
-//! reference signal (before any optional phase shifting). The second
-//! is 90 degrees out of phase (in quadrature) with the first
-//! copy. The demodulation signals are used to demodulate the ADC
 //! sampled signal.
-//! * _in-phase_ and _quadrature_ - These terms are used to delineate
-//! between the two components of the demodulation signal and the
-//! resulting two signals at any step downstream of the demodulation
-//! step. The in-phase signal is in-phase with the reference signal
-//! prior to any phase shifts. The quadrature signal is 90 degrees out
-//! of phase with the in-phase 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
@@ -44,24 +34,25 @@
 //!
 //! * `demodulate` - Computes the phase of the demodulation signal
 //! corresponding to each ADC sample, uses this phase to compute the
-//! in-phase and quadrature demodulation signals, and multiplies these
+//! demodulation signal, and multiplies this demodulation signal by
-//! demodulation signals by the ADC-sampled signal. This is a method
+//! the ADC-sampled signal. This is a method of `Lockin` since it
-//! of `Lockin` since it requires information about how to modify the
+//! requires information about how to modify the reference signal for
-//! reference signal for demodulation.
+//! demodulation.
-//! * `filter` - Performs IIR biquad filtering of in-phase and
+//! * `filter` - Performs IIR biquad filtering of a complex
-//! quadrature signals. This is commonly performed on the in-phase and
+//! signals. This is commonly performed on the signal provided by the
-//! quadrature components provided by the demodulation step, but can
+//! demodulation step, but can be performed at any other point in the
-//! be performed at any other point in the processing chain or omitted
+//! processing chain or omitted entirely. `filter` is a method of
-//! entirely. `filter` is a method of `Lockin` since it must hold onto
+//! `Lockin` since it must hold onto the filter configuration and
-//! the filter configuration and state.
+//! state.
-//! * `decimate` - This decimates the in-phase and quadrature signals
+//! * `decimate` - This decimates a signal to reduce the load on the
-//! to reduce the load on the DAC output. It does not require any
+//! DAC output. It does not require any state information and is
-//! state information and is therefore a normal function.
+//! 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::complex::Complex;
 use super::iir::{IIRState, IIR};
 use core::f32::consts::PI;
 
@@ -139,8 +130,7 @@ impl Lockin {
         }
     }
 
-    /// Demodulate an input signal with in-phase and quadrature
+    /// Demodulate an input signal with the complex reference signal.
-    /// reference signals.
     ///
     /// # Arguments
     ///
@@ -151,9 +141,9 @@ impl Lockin {
     ///
     /// # Returns
     ///
-    /// The demodulated in-phase and quadrature signals as an
+    /// The demodulated complex signal as a `Result`. When there are
-    /// `Option`. When there are an insufficient number of timestamps
+    /// an insufficient number of timestamps to perform processing,
-    /// to perform processing, `None` is returned.
+    /// `Err` is returned.
     ///
     /// # Assumptions
     ///
@@ -165,10 +155,7 @@ impl Lockin {
         &mut self,
         adc_samples: &[i16],
         timestamps: &[u16],
-    ) -> Result<
+    ) -> Result<[Complex; ADC_SAMPLE_BUFFER_SIZE], &str> {
-        ([f32; ADC_SAMPLE_BUFFER_SIZE], [f32; ADC_SAMPLE_BUFFER_SIZE]),
-        &str,
-    > {
         // update old timestamps for new ADC batch
         let sample_period = self.sample_period as i32;
         self.timestamps.iter_mut().for_each(|t| match *t {
@@ -200,14 +187,12 @@ impl Lockin {
         // compute ADC sample phases, sines/cosines and demodulate
         let reference_period =
             self.timestamps[0].unwrap() - self.timestamps[1].unwrap();
-        let mut in_phase = [0f32; ADC_SAMPLE_BUFFER_SIZE];
+        let mut signal = [Complex::new(0., 0.); ADC_SAMPLE_BUFFER_SIZE];
-        let mut quadrature = [0f32; ADC_SAMPLE_BUFFER_SIZE];
+        signal
-        in_phase
             .iter_mut()
-            .zip(quadrature.iter_mut())
             .zip(adc_samples.iter())
             .enumerate()
-            .for_each(|(n, ((i, q), sample))| {
+            .for_each(|(n, (s, sample))| {
                 let integer_phase: i32 = (n as i32 * self.sample_period as i32
                     - self.timestamps[0].unwrap())
                     * self.harmonic as i32;
@@ -215,104 +200,90 @@ impl Lockin {
                     + 2. * PI * integer_phase as f32 / reference_period as f32;
                 let (sine, cosine) = libm::sincosf(phase);
                 let sample = *sample as f32;
-                *i = sine * sample;
+                s.re = sine * sample;
-                *q = cosine * sample;
+                s.im = cosine * sample;
             });
 
-        Ok((in_phase, quadrature))
+        Ok(signal)
     }
 
-    /// Filter the in-phase and quadrature signals using the supplied
+    /// Filter the complex signal using the supplied biquad IIR. The
-    /// biquad IIR. The signal arrays are modified in place.
+    /// signal array is modified in place.
     ///
     /// # Arguments
     ///
-    /// * `in_phase` - In-phase signal.
+    /// * `signal` - Complex signal to filter.
-    /// * `quadrature` - Quadrature signal.
+    pub fn filter(&mut self, signal: &mut [Complex]) {
-    pub fn filter(&mut self, in_phase: &mut [f32], quadrature: &mut [f32]) {
+        signal.iter_mut().for_each(|s| {
-        in_phase
+            s.re = self.iir.update(&mut self.iirstate[0], s.re);
-            .iter_mut()
+            s.im = self.iir.update(&mut self.iirstate[1], s.im);
-            .zip(quadrature.iter_mut())
-            .for_each(|(i, q)| {
-                *i = self.iir.update(&mut self.iirstate[0], *i);
-                *q = self.iir.update(&mut self.iirstate[1], *q);
         });
     }
 }
 
-/// Decimate the in-phase and quadrature signals to
+/// Decimate the complex signal to `DECIMATED_BUFFER_SIZE`. The ratio
-/// `DECIMATED_BUFFER_SIZE`. The ratio of `ADC_SAMPLE_BUFFER_SIZE` to
+/// of `ADC_SAMPLE_BUFFER_SIZE` to `DECIMATED_BUFFER_SIZE` must be a
-/// `DECIMATED_BUFFER_SIZE` must be a power of 2.
+/// power of 2.
 ///
 /// # Arguments
 ///
-/// * `in_phase` - In-phase signal.
+/// * `signal` - Complex signal to decimate.
-/// * `quadrature` - Quadrature signal.
 ///
 /// # Returns
 ///
-/// The decimated in-phase and quadrature signals.
+/// The decimated signal.
 pub fn decimate(
-    in_phase: [f32; ADC_SAMPLE_BUFFER_SIZE],
+    signal: [Complex; ADC_SAMPLE_BUFFER_SIZE],
-    quadrature: [f32; ADC_SAMPLE_BUFFER_SIZE],
+) -> [Complex; DECIMATED_BUFFER_SIZE] {
-) -> ([f32; DECIMATED_BUFFER_SIZE], [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 in_phase_decimated = [0f32; DECIMATED_BUFFER_SIZE];
+    let mut signal_decimated = [Complex::new(0., 0.); DECIMATED_BUFFER_SIZE];
-    let mut quadrature_decimated = [0f32; DECIMATED_BUFFER_SIZE];
 
-    in_phase_decimated
+    signal_decimated
         .iter_mut()
-        .zip(quadrature_decimated.iter_mut())
+        .zip(signal.iter().step_by(n_k))
-        .zip(
+        .for_each(|(s_d, s)| {
-            in_phase
+            s_d.re = s.re;
-                .iter()
+            s_d.im = s.im;
-                .step_by(n_k)
-                .zip(quadrature.iter().step_by(n_k)),
-        )
-        .for_each(|((i_d, q_d), (i, q))| {
-            *i_d = *i;
-            *q_d = *q;
         });
 
-    (in_phase_decimated, quadrature_decimated)
+    signal_decimated
 }
 
-/// Compute the magnitude and phase from the in-phase and quadrature
+/// Compute the magnitude and phase from the complex signal. The
-/// signals. The in-phase and quadrature arrays are modified in place.
+/// signal array is modified in place.
 ///
 /// # Arguments
 ///
-/// * `in_phase` - In-phase signal.
+/// * `signal` - Complex signal to decimate.
-/// * `quadrature` - Quadrature signal.
+pub fn magnitude_phase(signal: &mut [Complex]) {
-pub fn magnitude_phase(in_phase: &mut [f32], quadrature: &mut [f32]) {
+    signal.iter_mut().for_each(|s| {
-    in_phase
+        let new_i = s.abs();
-        .iter_mut()
+        let new_q = s.arg();
-        .zip(quadrature.iter_mut())
+        s.re = new_i;
-        .for_each(|(i, q)| {
+        s.im = new_q;
-            let new_i = libm::sqrtf([*i, *q].iter().map(|i| i * i).sum());
-            let new_q = libm::atan2f(*q, *i);
-            *i = new_i;
-            *q = new_q;
     });
 }
 
 #[cfg(test)]
 mod tests {
     use super::*;
-    extern crate std;
 
     fn f32_is_close(a: f32, b: f32) -> bool {
         (a - b).abs() <= a.abs().max(b.abs()) * f32::EPSILON
     }
 
-    fn f32_array_is_close(a: &[f32], b: &[f32]) -> bool {
+    fn complex_is_close(a: Complex, b: Complex) -> bool {
+        f32_is_close(a.re, b.re) && f32_is_close(a.im, b.im)
+    }
+
+    fn complex_array_is_close(a: &[Complex], b: &[Complex]) -> bool {
         let mut result: bool = true;
         a.iter().zip(b.iter()).for_each(|(i, j)| {
-            result &= f32_is_close(*i, *j);
+            result &= complex_is_close(*i, *j);
         });
         result
     }
@@ -327,16 +298,30 @@ mod tests {
             <= a.abs().max(b.abs()) * relative_tolerance + fixed_tolerance
     }
 
-    fn array_within_tolerance(
+    fn complex_within_tolerance(
-        a: &[f32],
+        a: Complex,
-        b: &[f32],
+        b: Complex,
+        relative_tolerance: f32,
+        fixed_tolerance: f32,
+    ) -> bool {
+        within_tolerance(a.re, b.re, relative_tolerance, fixed_tolerance)
+            && within_tolerance(a.im, b.im, relative_tolerance, fixed_tolerance)
+    }
+
+    fn complex_array_within_tolerance(
+        a: &[Complex],
+        b: &[Complex],
         relative_tolerance: f32,
         fixed_tolerance: f32,
     ) -> bool {
         let mut result: bool = true;
         a.iter().zip(b.iter()).for_each(|(i, j)| {
-            result &=
+            result &= complex_within_tolerance(
-                within_tolerance(*i, *j, relative_tolerance, fixed_tolerance);
+                *i,
+                *j,
+                relative_tolerance,
+                fixed_tolerance,
+            );
         });
         result
     }
@@ -354,75 +339,93 @@ mod tests {
 
     #[test]
     fn magnitude_phase_length_1_quadrant_1() {
-        let mut in_phase: [f32; 1] = [1.];
+        let mut signal: [Complex; 1] = [Complex::new(1., 1.)];
-        let mut quadrature: [f32; 1] = [1.];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[2_f32.sqrt()]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[PI / 4.]));
+            &[Complex::new(2_f32.sqrt(), PI / 4.)]
+        ));
 
-        in_phase = [3_f32.sqrt() / 2.];
+        signal = [Complex::new(3_f32.sqrt() / 2., 1. / 2.)];
-        quadrature = [1. / 2.];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[1_f32]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[PI / 6.]));
+            &[Complex::new(1., PI / 6.)]
+        ));
     }
 
     #[test]
     fn magnitude_phase_length_1_quadrant_2() {
-        let mut in_phase: [f32; 1] = [-1.];
+        let mut signal = [Complex::new(-1., 1.)];
-        let mut quadrature: [f32; 1] = [1.];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[2_f32.sqrt()]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[3. * PI / 4.]));
+            &[Complex::new(2_f32.sqrt(), 3. * PI / 4.)]
+        ));
 
-        in_phase = [-1. / 2.];
+        signal = [Complex::new(-1. / 2., 3_f32.sqrt() / 2.)];
-        quadrature = [3_f32.sqrt() / 2.];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[1_f32]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[2. * PI / 3.]));
+            &[Complex::new(1_f32, 2. * PI / 3.)]
+        ));
     }
 
     #[test]
     fn magnitude_phase_length_1_quadrant_3() {
-        let mut in_phase: [f32; 1] = [-1. / 2_f32.sqrt()];
+        let mut signal = [Complex::new(-1. / 2_f32.sqrt(), -1. / 2_f32.sqrt())];
-        let mut quadrature: [f32; 1] = [-1. / 2_f32.sqrt()];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[1_f32.sqrt()]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[-3. * PI / 4.]));
+            &[Complex::new(1_f32.sqrt(), -3. * PI / 4.)]
+        ));
 
-        in_phase = [-1. / 2.];
+        signal = [Complex::new(-1. / 2., -2_f32.sqrt())];
-        quadrature = [-2_f32.sqrt()];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[(3. / 2.) as f32]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[-1.91063323625 as f32]));
+            &[Complex::new((3. / 2.) as f32, -1.91063323625 as f32)]
+        ));
     }
 
     #[test]
     fn magnitude_phase_length_1_quadrant_4() {
-        let mut in_phase: [f32; 1] = [1. / 2_f32.sqrt()];
+        let mut signal = [Complex::new(1. / 2_f32.sqrt(), -1. / 2_f32.sqrt())];
-        let mut quadrature: [f32; 1] = [-1. / 2_f32.sqrt()];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[1_f32.sqrt()]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[-1. * PI / 4.]));
+            &[Complex::new(1_f32.sqrt(), -1. * PI / 4.)]
+        ));
 
-        in_phase = [3_f32.sqrt() / 2.];
+        signal = [Complex::new(3_f32.sqrt() / 2., -1. / 2.)];
-        quadrature = [-1. / 2.];
+        magnitude_phase(&mut signal);
-        magnitude_phase(&mut in_phase, &mut quadrature);
+        assert!(complex_array_is_close(
-        assert!(f32_array_is_close(&in_phase, &[1_f32]));
+            &signal,
-        assert!(f32_array_is_close(&quadrature, &[-PI / 6.]));
+            &[Complex::new(1_f32, -PI / 6.)]
+        ));
     }
 
     #[test]
     fn decimate_sample_16_decimated_1() {
-        let in_phase: [f32; ADC_SAMPLE_BUFFER_SIZE] = [
+        let signal: [Complex; ADC_SAMPLE_BUFFER_SIZE] = [
-            0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2,
+            Complex::new(0.0, 1.6),
-            1.3, 1.4, 1.5,
+            Complex::new(0.1, 1.7),
+            Complex::new(0.2, 1.8),
+            Complex::new(0.3, 1.9),
+            Complex::new(0.4, 2.0),
+            Complex::new(0.5, 2.1),
+            Complex::new(0.6, 2.2),
+            Complex::new(0.7, 2.3),
+            Complex::new(0.8, 2.4),
+            Complex::new(0.9, 2.5),
+            Complex::new(1.0, 2.6),
+            Complex::new(1.1, 2.7),
+            Complex::new(1.2, 2.8),
+            Complex::new(1.3, 2.9),
+            Complex::new(1.4, 3.0),
+            Complex::new(1.5, 3.1),
         ];
-        let quadrature: [f32; ADC_SAMPLE_BUFFER_SIZE] = [
+        assert_eq!(decimate(signal), [Complex::new(0.0, 1.6)]);
-            1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8,
-            2.9, 3.0, 3.1,
-        ];
-        assert_eq!(decimate(in_phase, quadrature), ([0.0], [1.6]));
     }
 
     #[test]
@@ -439,7 +442,7 @@ mod tests {
             },
         );
         assert_eq!(
-            lockin.demodulate(&[0; ADC_SAMPLE_BUFFER_SIZE], &[],),
+            lockin.demodulate(&[0; ADC_SAMPLE_BUFFER_SIZE], &[]),
             Err("insufficient timestamps")
         );
     }
@@ -489,32 +492,20 @@ mod tests {
             -(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 in_phase: [f32; ADC_SAMPLE_BUFFER_SIZE] =
+        let mut signal = [Complex::new(0., 0.); ADC_SAMPLE_BUFFER_SIZE];
-            [0.; ADC_SAMPLE_BUFFER_SIZE];
+        for (n, s) in signal.iter_mut().enumerate() {
-        let mut quadrature: [f32; ADC_SAMPLE_BUFFER_SIZE] =
-            [0.; ADC_SAMPLE_BUFFER_SIZE];
-        for (n, (i, q)) in
-            in_phase.iter_mut().zip(quadrature.iter_mut()).enumerate()
-        {
             let adc_phase = initial_phase + n as f32 * phase_increment;
             let sine = adc_phase.sin();
             let cosine = adc_phase.cos();
-            *i = sine * adc_samples[n] as f32;
+            s.re = sine * adc_samples[n] as f32;
-            *q = cosine * adc_samples[n] as f32;
+            s.im = cosine * adc_samples[n] as f32;
         }
-        let (result_in_phase, result_quadrature) =
+        let result = lockin.demodulate(&adc_samples, timestamps).unwrap();
-            lockin.demodulate(&adc_samples, timestamps).unwrap();
         assert!(
-            array_within_tolerance(&result_in_phase, &in_phase, 0., 1e-5),
+            complex_array_within_tolerance(&result, &signal, 0., 1e-5),
-            "\nin_phase computed: {:?},\nin_phase expected: {:?}",
+            "\nsignal computed: {:?},\nsignal expected: {:?}",
-            result_in_phase,
+            result,
-            in_phase
+            signal
-        );
-        assert!(
-            array_within_tolerance(&result_quadrature, &quadrature, 0., 1e-5),
-            "\nquadrature computed: {:?},\nquadrature expected: {:?}",
-            result_quadrature,
-            quadrature
         );
     }
 }

dsp/tests/lockin_low_pass.rs

@@ -1,3 +1,4 @@
+use dsp::complex::Complex;
 use dsp::iir::IIR;
 use dsp::lockin::{
     decimate, magnitude_phase, Lockin, ADC_SAMPLE_BUFFER_SIZE,
@@ -582,7 +583,7 @@ fn lowpass_test(
     pure_signals.push(desired_input);
 
     for n in 0..(samples + extra_samples) {
-        let signal: [i16; ADC_SAMPLE_BUFFER_SIZE] = adc_sampled_signal(
+        let adc_signal: [i16; ADC_SAMPLE_BUFFER_SIZE] = adc_sampled_signal(
             &pure_signals,
             timestamp_start,
             internal_frequency,
@@ -597,33 +598,31 @@ fn lowpass_test(
             internal_frequency,
         );
 
-        let mut in_phase: [f32; ADC_SAMPLE_BUFFER_SIZE];
+        let mut signal: [Complex; ADC_SAMPLE_BUFFER_SIZE];
-        let mut quadrature: [f32; ADC_SAMPLE_BUFFER_SIZE];
+        match lockin.demodulate(&adc_signal, timestamps) {
-        match lockin.demodulate(&signal, timestamps) {
+            Ok(s) => {
-            Ok((i, q)) => {
+                signal = s;
-                in_phase = i;
-                quadrature = q;
             }
             Err(_) => {
                 continue;
             }
         }
 
-        lockin.filter(&mut in_phase, &mut quadrature);
+        lockin.filter(&mut signal);
-        let (in_phase_decimated, quadrature_decimated) =
+        let signal_decimated = decimate(signal);
-            decimate(in_phase, quadrature);
 
-        let mut magnitude_decimated = in_phase_decimated.clone();
+        let mut magnitude_phase_decimated = signal.clone();
-        let mut phase_decimated = quadrature_decimated.clone();
+        // let mut magnitude_decimated = in_phase_decimated.clone();
+        // let mut phase_decimated = quadrature_decimated.clone();
 
-        magnitude_phase(&mut magnitude_decimated, &mut phase_decimated);
+        magnitude_phase(&mut magnitude_phase_decimated);
 
         // Ensure stable within tolerance for 1 time constant after
         // `time_constant_factor`.
         if n >= samples {
             for k in 0..DECIMATED_BUFFER_SIZE {
                 let amplitude_normalized: f32 =
-                    magnitude_decimated[k] / ADC_MAX_COUNT as f32;
+                    magnitude_phase_decimated[k].re / ADC_MAX_COUNT as f32;
                 assert!(
                     tolerance_check(linear(desired_input.amplitude_dbfs) as f32, amplitude_normalized, total_magnitude_noise as f32, tolerance),
                     "magnitude actual: {:.4} ({:.2} dBFS), magnitude computed: {:.4} ({:.2} dBFS), tolerance: {:.4}",
@@ -636,13 +635,13 @@ fn lowpass_test(
                 assert!(
                     tolerance_check(
                         effective_phase_offset as f32,
-                        phase_decimated[k],
+                        magnitude_phase_decimated[k].im,
                         total_phase_noise as f32,
                         tolerance
                     ),
                     "phase actual: {:.4}, phase computed: {:.4}, tolerance: {:.4}",
                     effective_phase_offset as f32,
-                    phase_decimated[k],
+                    magnitude_phase_decimated[k].im,
                     max_error(
                         effective_phase_offset as f32,
                         total_phase_noise as f32,
@@ -651,9 +650,9 @@ fn lowpass_test(
                 );
 
                 let in_phase_normalized: f32 =
-                    in_phase_decimated[k] / ADC_MAX_COUNT as f32;
+                    signal_decimated[k].re / ADC_MAX_COUNT as f32;
                 let quadrature_normalized: f32 =
-                    quadrature_decimated[k] / ADC_MAX_COUNT as f32;
+                    signal_decimated[k].im / ADC_MAX_COUNT as f32;
                 assert!(
                     tolerance_check(
                         in_phase_actual as f32,