diff --git a/dsp/tests/lockin.rs b/dsp/tests/lockin.rs
new file mode 100644
index 0000000..896f871
--- /dev/null
+++ b/dsp/tests/lockin.rs
@@ -0,0 +1,1215 @@
+use dsp::{
+    iir_int::{IIRState, IIR},
+    reciprocal_pll::TimestampHandler,
+    shift_round,
+    trig::{atan2, cossin},
+    Complex,
+};
+
+use std::f64::consts::PI;
+use std::vec::Vec;
+
+const ADC_MAX: f64 = 1.;
+const ADC_MAX_COUNT: f64 = (1 << 15) as f64;
+
+struct Lockin {
+    harmonic: u32,
+    phase_offset: u32,
+    iir: IIR,
+    iir_state: [IIRState; 2],
+}
+
+impl Lockin {
+    /// Construct a new `Lockin` instance.
+    ///
+    /// # Args
+    /// * `harmonic` - Factor for harmonic demodulation. For example, a value of 1 would demodulate
+    /// with the reference frequency whereas a value of 2 would demodulate with the first harmonic
+    /// of the reference frequency.
+    /// * `phase_offset` - Phase offset of the scaled (see `harmonic`) demodulation signal relative
+    /// to the reference signal.
+    /// * `iir` - IIR coefficients (see `iir_int::IIR`) used for filtering the demodulated in-phase
+    /// and quadrature signals.
+    pub fn new(harmonic: u32, phase_offset: u32, iir: IIR) -> Self {
+        Lockin {
+            harmonic,
+            phase_offset,
+            iir,
+            iir_state: [[0; 5]; 2],
+        }
+    }
+
+    /// Compute the in-phase and quadrature signals. This is intended to mimic the lock-in
+    /// processing routine invoked in main.rs.
+    ///
+    /// # Args
+    /// * `adc_samples` - ADC samples.
+    /// * `demodulation_initial_phase` - Phase value of the demodulation signal corresponding to the
+    /// first ADC sample.
+    /// * `demodulation_frequency` - Demodulation frequency.
+    pub fn update(
+        &mut self,
+        adc_samples: Vec<i16>,
+        demodulation_initial_phase: u32,
+        demodulation_frequency: u32,
+    ) -> Complex<i32> {
+        let mut signal = Vec::<Complex<i32>>::new();
+
+        adc_samples.iter().enumerate().for_each(|(i, s)| {
+            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);
+
+            signal.push((
+                *s as i32 * shift_round(sin, 16),
+                *s as i32 * shift_round(cos, 16),
+            ));
+
+            signal[i].0 = self.iir.update(&mut self.iir_state[0], signal[i].0);
+            signal[i].1 = self.iir.update(&mut self.iir_state[1], signal[i].1);
+        });
+
+        (signal[0].0, signal[0].1)
+    }
+}
+
+/// Single-frequency sinusoid.
+#[derive(Copy, Clone)]
+struct PureSine {
+    // Frequency (in Hz).
+    frequency: f64,
+    // Amplitude in dBFS (decibels relative to full-scale). A 16-bit ADC has a minimum dBFS for each
+    // sample of -90.
+    amplitude_dbfs: f64,
+    // Phase offset (in radians).
+    phase_offset: f64,
+}
+
+/// Convert a dBFS voltage ratio to a linear ratio.
+///
+/// # Args
+/// * `dbfs` - dB ratio relative to full scale.
+///
+/// # Returns
+/// Linear value.
+fn linear(dbfs: f64) -> f64 {
+    let base = 10_f64;
+    ADC_MAX * base.powf(dbfs / 20.)
+}
+
+/// Convert a linear voltage ratio to a dBFS ratio.
+///
+/// # Args
+/// * `linear` - Linear voltage ratio.
+///
+/// # Returns
+/// dBFS value.
+fn dbfs(linear: f64) -> f64 {
+    20. * (linear / ADC_MAX).log10()
+}
+
+/// Convert a real ADC input value in the range `-ADC_MAX` to `+ADC_MAX` to an equivalent 16-bit ADC
+/// sampled value. This models the ideal ADC transfer function.
+///
+/// # Args
+/// * `x` - Real ADC input value.
+///
+/// # Returns
+/// Sampled ADC value.
+fn real_to_adc_sample(x: f64) -> i16 {
+    let max: i32 = i16::MAX as i32;
+    let min: i32 = i16::MIN as i32;
+
+    let xi: i32 = (x / ADC_MAX * ADC_MAX_COUNT) as i32;
+
+    // It's difficult to characterize the correct output result when the inputs are clipped, so
+    // panic instead.
+    if xi > max {
+        panic!("Input clipped to maximum, result is unlikely to be correct.");
+    } else if xi < min {
+        panic!("Input clipped to minimum, result is unlikely to be correct.");
+    }
+
+    xi as i16
+}
+
+/// Generate a full batch of ADC samples starting at `timestamp_start`.
+///
+/// # Args
+/// * `pure_signals` - Pure sinusoidal components of the ADC-sampled signal.
+/// * `timestamp_start` - Starting time of ADC-sampled signal in terms of the internal clock count.
+/// * `internal_frequency` - Internal clock frequency (in Hz).
+/// * `adc_frequency` - ADC sampling frequency (in Hz).
+/// * `sample_buffer_size` - The number of ADC samples in one processing batch.
+///
+/// # Returns
+/// The sampled signal at the ADC input.
+fn adc_sampled_signal(
+    pure_signals: &Vec<PureSine>,
+    timestamp_start: u64,
+    internal_frequency: f64,
+    adc_frequency: f64,
+    sample_buffer_size: u32,
+) -> Vec<i16> {
+    // amplitude of each pure signal
+    let mut amplitude: Vec<f64> = Vec::<f64>::new();
+    // initial phase value for each pure signal
+    let mut initial_phase: Vec<f64> = Vec::<f64>::new();
+    // phase increment at each ADC sample for each pure signal
+    let mut phase_increment: Vec<f64> = Vec::<f64>::new();
+    let adc_period = internal_frequency / adc_frequency;
+
+    // For each pure sinusoid, compute the amplitude, phase corresponding to the first ADC sample,
+    // and phase increment for each subsequent ADC sample.
+    for pure_signal in pure_signals.iter() {
+        let signal_period = internal_frequency / pure_signal.frequency;
+        let phase_offset_count =
+            pure_signal.phase_offset / (2. * PI) * signal_period;
+        let initial_phase_count =
+            (phase_offset_count + timestamp_start as f64) % signal_period;
+
+        amplitude.push(linear(pure_signal.amplitude_dbfs));
+        initial_phase.push(2. * PI * initial_phase_count / signal_period);
+        phase_increment.push(2. * PI * adc_period / signal_period);
+    }
+
+    // Compute the input signal corresponding to each ADC sample by summing the contributions from
+    // each pure sinusoid.
+    let mut signal = Vec::<i16>::new();
+
+    for i in 0..sample_buffer_size {
+        signal.push(real_to_adc_sample(
+            amplitude
+                .iter()
+                .zip(initial_phase.iter())
+                .zip(phase_increment.iter())
+                .fold(0., |acc, ((a, phi), theta)| {
+                    acc + a * (phi + theta * i as f64).sin()
+                }),
+        ));
+    }
+
+    signal
+}
+
+/// Reference clock timestamp values in one ADC batch period starting at `timestamp_start`. The
+/// number of timestamps in a batch can be 0 or 1, so this returns an Option containing a timestamp
+/// only if one occurred during the batch.
+///
+/// # Args
+/// * `reference_frequency` - External reference signal frequency (in Hz).
+/// * `timestamp_start` - Start time in terms of the internal clock count. This is the start time of
+/// the current processing sequence.
+/// * `timestamp_stop` - Stop time in terms of the internal clock count.
+/// * `internal_frequency` - Internal clock frequency (in Hz).
+///
+/// # Returns
+/// An Option, containing a timestamp if one occurred during the current batch period.
+fn adc_batch_timestamps(
+    reference_frequency: f64,
+    timestamp_start: u64,
+    timestamp_stop: u64,
+    internal_frequency: f64,
+) -> Option<u32> {
+    let reference_period = internal_frequency / reference_frequency;
+    let start_count = timestamp_start as f64 % reference_period;
+
+    let timestamp = (reference_period - start_count) % reference_period;
+
+    if timestamp < (timestamp_stop - timestamp_start) as f64 {
+        return Some(
+            ((timestamp_start + timestamp.round() as u64) % (1u64 << 32))
+                as u32,
+        );
+    }
+
+    None
+}
+
+/// Lowpass biquad filter using cutoff and sampling frequencies.  Taken from:
+/// https://webaudio.github.io/Audio-EQ-Cookbook/audio-eq-cookbook.html
+///
+/// # Args
+/// * `corner_frequency` - Corner frequency, or 3dB cutoff frequency (in Hz).
+/// * `sampling_frequency` - Sampling frequency (in Hz).
+///
+/// # Returns
+/// 2nd-order IIR filter coefficients in the form [b0,b1,b2,a1,a2]. a0 is set to -1.
+fn lowpass_iir_coefficients(
+    corner_frequency: f64,
+    sampling_frequency: f64,
+) -> [i32; 5] {
+    let normalized_angular_frequency: f64 =
+        2. * PI * corner_frequency / sampling_frequency;
+    let quality_factor: f64 = 1. / 2f64.sqrt();
+    let alpha: f64 = normalized_angular_frequency.sin() / (2. * quality_factor);
+    // All b coefficients have been multiplied by a factor of 2 in comparison with the link above in
+    // order to set the passband gain to 2.
+    let mut b0: f64 = 1. - normalized_angular_frequency.cos();
+    let mut b1: f64 = 2. * (1. - normalized_angular_frequency.cos());
+    let mut b2: f64 = b0;
+    let a0: f64 = 1. + alpha;
+    let mut a1: f64 = -2. * normalized_angular_frequency.cos();
+    let mut a2: f64 = 1. - alpha;
+    b0 /= a0;
+    b1 /= a0;
+    b2 /= a0;
+    a1 /= -a0;
+    a2 /= -a0;
+
+    // iir uses Q2.30 fixed point
+    [
+        (b0 * (1 << 30) as f64).round() as i32,
+        (b1 * (1 << 30) as f64).round() as i32,
+        (b2 * (1 << 30) as f64).round() as i32,
+        (a1 * (1 << 30) as f64).round() as i32,
+        (a2 * (1 << 30) as f64).round() as i32,
+    ]
+}
+
+/// Maximum acceptable error between a computed and actual value given fixed and relative
+/// tolerances.
+///
+/// # Args
+/// * `a` - First input.
+/// * `b` - Second input. The relative tolerance is computed with respect to the maximum of the
+/// absolute values of the first and second inputs.
+/// * `rtol` - Relative tolerance.
+/// * `atol` - Fixed tolerance.
+///
+/// # Returns
+/// Maximum acceptable error.
+fn max_error(a: f64, b: f64, rtol: f64, atol: f64) -> f64 {
+    rtol * a.abs().max(b.abs()) + atol
+}
+
+// TODO this is (mostly) copied from testing.rs.
+pub fn isclose(a: f64, b: f64, rtol: f64, atol: f64) -> bool {
+    (a - b).abs() <= max_error(a, b, rtol, atol)
+}
+
+/// Total noise amplitude of the input signal after sampling by the ADC. This computes an upper
+/// bound of the total noise amplitude, rather than its actual value.
+///
+/// # Args
+/// * `noise_inputs` - Noise sources at the ADC input.
+/// * `demodulation_frequency` - Frequency of the demodulation signal (in Hz).
+/// * `corner_frequency` - Low-pass filter 3dB corner (cutoff) frequency.
+///
+/// # Returns
+/// Upper bound of the total amplitude of all noise sources.
+fn sampled_noise_amplitude(
+    noise_inputs: &Vec<PureSine>,
+    demodulation_frequency: f64,
+    corner_frequency: f64,
+) -> f64 {
+    // There is not a simple way to compute the amplitude of a superpostition of sinusoids with
+    // different frequencies and phases. Although we can compute the amplitude in special cases
+    // (e.g., two signals whose periods have a common multiple), these do not help us in the general
+    // case. However, we can say that the total amplitude will not be greater than the sum of the
+    // amplitudes of the individual noise sources. We treat this as an upper bound, and use it as an
+    // approximation of the actual amplitude.
+
+    let mut noise: f64 = noise_inputs
+        .iter()
+        .map(|n| {
+            // Noise inputs create an oscillation at the output, where the oscillation magnitude is
+            // determined by the strength of the noise and its attenuation (attenuation is
+            // determined by its proximity to the demodulation frequency and filter rolloff).
+            let octaves = ((n.frequency - demodulation_frequency).abs()
+                / corner_frequency)
+                .log2();
+            // 2nd-order filter. Approximately 12dB/octave rolloff.
+            let attenuation = -2. * 20. * 2_f64.log10() * octaves;
+            linear(n.amplitude_dbfs + attenuation)
+        })
+        .sum();
+
+    // Add in 1/2 LSB for the maximum amplitude deviation resulting from quantization.
+    noise += 1. / ADC_MAX_COUNT / 2.;
+
+    noise
+}
+
+/// Compute the maximum effect of input noise on the lock-in magnitude computation.
+///
+/// The maximum effect of noise on the magnitude computation is given by:
+///
+/// | sqrt((I+n*sin(x))**2 + (Q+n*cos(x))**2) - sqrt(I**2 + Q**2) |
+///
+/// * I is the in-phase component of the portion of the input signal with the same frequency as the
+/// demodulation signal.
+/// * Q is the quadrature component.
+/// * n is the total noise amplitude (from all contributions, after attenuation from filtering).
+/// * x is the phase of the demodulation signal.
+///
+/// We need to find the demodulation phase (x) that maximizes this expression. We can ignore the
+/// absolute value operation by also considering the expression minimum. The locations of the
+/// minimum and maximum can be computed analytically by finding the value of x when the derivative
+/// of this expression with respect to x is 0. When we solve this equation, we find:
+///
+/// x = atan(I/Q)
+///
+/// It's worth noting that this solution is technically only valid when cos(x)!=0 (i.e.,
+/// x!=pi/2,-pi/2). However, this is not a problem because we only get these values when Q=0. Rust
+/// correctly computes atan(inf)=pi/2, which is precisely what we want because x=pi/2 maximizes
+/// sin(x) and therefore also the noise effect.
+///
+/// The other maximum or minimum is pi radians away from this value.
+///
+/// # Args
+/// * `total_noise_amplitude` - Combined amplitude of all noise sources sampled by the ADC.
+/// * `in_phase_actual` - Value of the in-phase component if no noise were present at the ADC input.
+/// * `quadrature_actual` - Value of the quadrature component if no noise were present at the ADC
+/// input.
+/// * `desired_input_amplitude` - Amplitude of the desired input signal. That is, the input signal
+/// component with the same frequency as the demodulation signal.
+///
+/// # Returns
+/// Approximation of the maximum effect on the magnitude computation due to noise sources at the ADC
+/// input.
+fn magnitude_noise(
+    total_noise_amplitude: f64,
+    in_phase_actual: f64,
+    quadrature_actual: f64,
+    desired_input_amplitude: f64,
+) -> f64 {
+    // See function documentation for explanation.
+    let noise = |in_phase_delta: f64, quadrature_delta: f64| -> f64 {
+        (((in_phase_actual + in_phase_delta).powf(2.)
+            + (quadrature_actual + quadrature_delta).powf(2.))
+        .sqrt()
+            - desired_input_amplitude)
+            .abs()
+    };
+
+    let phase = (in_phase_actual / quadrature_actual).atan();
+    let max_noise_1 = noise(
+        total_noise_amplitude * phase.sin(),
+        total_noise_amplitude * phase.cos(),
+    );
+    let max_noise_2 = noise(
+        total_noise_amplitude * (phase + PI).sin(),
+        total_noise_amplitude * (phase + PI).cos(),
+    );
+
+    max_noise_1.max(max_noise_2)
+}
+
+/// Compute the maximum phase deviation from the correct value due to the input noise sources.
+///
+/// The maximum effect of noise on the phase computation is given by:
+///
+/// | atan2(Q+n*cos(x), I+n*sin(x)) - atan2(Q, I) |
+///
+/// See `magnitude_noise` for an explanation of the terms in this mathematical expression.
+///
+/// This expression is harder to compute analytically than the expression in `magnitude_noise`. We
+/// could compute it numerically, but that's expensive. However, we can use heuristics to try to
+/// guess the values of x that will maximize the noise effect. Intuitively, the difference will be
+/// largest when the Y-argument of the atan2 function (Q+n*cos(x)) is pushed in the opposite
+/// direction of the noise effect on the X-argument (i.e., cos(x) and sin(x) have different
+/// signs). We can use:
+///
+/// * sin(x)=+-1 (+- denotes plus or minus), cos(x)=0,
+/// * sin(x)=0, cos(x)=+-1, and
+/// * the value of x that maximizes |sin(x)-cos(x)| (when sin(x)=1/sqrt(2) and cos(x)=-1/sqrt(2), or
+/// when the signs are flipped)
+///
+/// The first choice addresses cases in which |I|>>|Q|, the second choice addresses cases in which
+/// |Q|>>|I|, and the third choice addresses cases in which |I|~|Q|. We can test all of these cases
+/// as an approximation for the real maximum.
+///
+/// # Args
+/// * `total_noise_amplitude` - Total amplitude of all input noise sources.
+/// * `in_phase_actual` - Value of the in-phase component if no noise were present at the input.
+/// * `quadrature_actual` - Value of the quadrature component if no noise were present at the input.
+///
+/// # Returns
+/// Approximation of the maximum effect on the phase computation due to noise sources at the ADC
+/// input.
+fn phase_noise(
+    total_noise_amplitude: f64,
+    in_phase_actual: f64,
+    quadrature_actual: f64,
+) -> f64 {
+    // See function documentation for explanation.
+    let noise = |in_phase_delta: f64, quadrature_delta: f64| -> f64 {
+        ((quadrature_actual + quadrature_delta)
+            .atan2(in_phase_actual + in_phase_delta)
+            - quadrature_actual.atan2(in_phase_actual))
+        .abs()
+    };
+
+    let mut max_noise: f64 = 0.;
+    for (in_phase_delta, quadrature_delta) in [
+        (
+            total_noise_amplitude / 2_f64.sqrt(),
+            total_noise_amplitude / -2_f64.sqrt(),
+        ),
+        (
+            total_noise_amplitude / -2_f64.sqrt(),
+            total_noise_amplitude / 2_f64.sqrt(),
+        ),
+        (total_noise_amplitude, 0.),
+        (-total_noise_amplitude, 0.),
+        (0., total_noise_amplitude),
+        (0., -total_noise_amplitude),
+    ]
+    .iter()
+    {
+        max_noise = max_noise.max(noise(*in_phase_delta, *quadrature_delta));
+    }
+
+    max_noise
+}
+
+/// Lowpass filter test for in-phase/quadrature and magnitude/phase computations.
+///
+/// This attempts to "intelligently" model acceptable tolerance ranges for the measured in-phase,
+/// quadrature, magnitude and phase results of lock-in processing for a typical low-pass filter
+/// application. So, instead of testing whether the lock-in processing extracts the true magnitude
+/// and phase (or in-phase and quadrature components) of the input signal, it attempts to calculate
+/// what the lock-in processing should compute given any set of input noise sources. For example, if
+/// a noise source of sufficient strength differs in frequency by 1kHz from the reference frequency
+/// and the filter cutoff frequency is also 1kHz, testing if the lock-in amplifier extracts the
+/// amplitude and phase of the input signal whose frequency is equal to the demodulation frequency
+/// is doomed to failure. Instead, this function tests whether the lock-in correctly adheres to its
+/// actual transfer function, whether or not it was given reasonable inputs. The logic for computing
+/// acceptable tolerance ranges is performed in `sampled_noise_amplitude`, `magnitude_noise`, and
+/// `phase_noise`.
+///
+/// # Args
+/// * `internal_frequency` - Internal clock frequency (Hz). The internal clock increments timestamp
+/// counter values used to record the edges of the external reference.
+/// * `adc_frequency` - ADC sampling frequency (in Hz).
+/// * `reference_frequency` - External reference frequency (in Hz).
+/// * `demodulation_phase_offset` - Phase offset applied to the in-phase and quadrature demodulation
+/// signals.
+/// * `harmonic` - Scaling factor for the demodulation frequency. E.g., 2 would demodulate with the
+/// first harmonic of the reference frequency.
+/// * `sample_buffer_size_log2` - The base-2 logarithm of the number of samples in a processing
+/// batch.
+/// * `pll_shift_frequency` - See `pll::update()`.
+/// * `pll_shift_phase` - See `pll::update()`.
+/// * `corner_frequency` - Lowpass filter 3dB cutoff frequency.
+/// * `desired_input` - `PureSine` giving the frequency, amplitude and phase of the desired result.
+/// * `noise_inputs` - Vector of `PureSine` for any noise inputs on top of `desired_input`.
+/// * `time_constant_factor` - Number of time constants after which the output is considered valid.
+/// * `tolerance` - Acceptable relative tolerance for the magnitude and angle outputs. This is added
+/// to fixed tolerance values computed inside this function. The outputs must remain within this
+/// tolerance between `time_constant_factor` and `time_constant_factor+1` time constants.
+fn lowpass_test(
+    internal_frequency: f64,
+    adc_frequency: f64,
+    reference_frequency: f64,
+    demodulation_phase_offset: f64,
+    harmonic: u32,
+    sample_buffer_size_log2: usize,
+    pll_shift_frequency: u8,
+    pll_shift_phase: u8,
+    corner_frequency: f64,
+    desired_input: PureSine,
+    noise_inputs: &mut Vec<PureSine>,
+    time_constant_factor: f64,
+    tolerance: f64,
+) {
+    assert!(
+        isclose((internal_frequency / adc_frequency).log2(), (internal_frequency / adc_frequency).log2().round(), 0., 1e-5),
+        "The number of internal clock cycles in one ADC sampling period must be a power-of-two."
+    );
+
+    assert!(
+        internal_frequency / reference_frequency
+            >= internal_frequency / adc_frequency
+            * (1 << sample_buffer_size_log2) as f64,
+        "Too many timestamps per batch. Each batch can have at most 1 timestamp."
+    );
+
+    let adc_sample_ticks_log2 =
+        (internal_frequency / adc_frequency).log2().round() as usize;
+    assert!(
+        adc_sample_ticks_log2 + sample_buffer_size_log2 <= 32,
+        "The base-2 log of the number of ADC ticks in a sampling period plus the base-2 log of the sample buffer size must be less than 32."
+    );
+
+    let mut lockin = Lockin::new(
+        harmonic,
+        (demodulation_phase_offset / (2. * PI) * (1_u64 << 32) as f64).round()
+            as u32,
+        IIR {
+            ba: lowpass_iir_coefficients(corner_frequency, adc_frequency),
+        },
+    );
+    let mut timestamp_handler = TimestampHandler::new(
+        pll_shift_frequency,
+        pll_shift_phase,
+        adc_sample_ticks_log2,
+        sample_buffer_size_log2,
+    );
+
+    let mut timestamp_start: u64 = 0;
+    let time_constant: f64 = 1. / (2. * PI * corner_frequency);
+    // Account for the pll settling time (see its documentation).
+    let pll_time_constant_samples =
+        (1 << pll_shift_phase.max(pll_shift_frequency)) as usize;
+    let low_pass_time_constant_samples =
+        (time_constant_factor * time_constant * adc_frequency
+            / (1 << sample_buffer_size_log2) as f64) as usize;
+    let samples = pll_time_constant_samples + low_pass_time_constant_samples;
+    // Ensure the result remains within tolerance for 1 time constant after `time_constant_factor`
+    // time constants.
+    let extra_samples = (time_constant * adc_frequency) as usize;
+    let batch_sample_count =
+        1_u64 << (adc_sample_ticks_log2 + sample_buffer_size_log2);
+
+    let effective_phase_offset =
+        desired_input.phase_offset - demodulation_phase_offset;
+    let in_phase_actual =
+        linear(desired_input.amplitude_dbfs) * effective_phase_offset.cos();
+    let quadrature_actual =
+        linear(desired_input.amplitude_dbfs) * effective_phase_offset.sin();
+
+    let total_noise_amplitude = sampled_noise_amplitude(
+        noise_inputs,
+        reference_frequency * harmonic as f64,
+        corner_frequency,
+    );
+    // Add some fixed error to account for errors introduced by the PLL, our custom trig functions
+    // and integer division. It's a bit difficult to be precise about this. I've added a 1%
+    // (relative to full scale) error.
+    let total_magnitude_noise = magnitude_noise(
+        total_noise_amplitude,
+        in_phase_actual,
+        quadrature_actual,
+        linear(desired_input.amplitude_dbfs),
+    ) + 1e-2;
+    let total_phase_noise =
+        phase_noise(total_noise_amplitude, in_phase_actual, quadrature_actual)
+            + 1e-2 * 2. * PI;
+
+    let pure_signals = noise_inputs;
+    pure_signals.push(desired_input);
+
+    for n in 0..(samples + extra_samples) {
+        let adc_signal = adc_sampled_signal(
+            &pure_signals,
+            timestamp_start,
+            internal_frequency,
+            adc_frequency,
+            1 << sample_buffer_size_log2,
+        );
+        let timestamp = adc_batch_timestamps(
+            reference_frequency,
+            timestamp_start,
+            timestamp_start + batch_sample_count - 1,
+            internal_frequency,
+        );
+
+        let (demodulation_initial_phase, demodulation_frequency) =
+            timestamp_handler.update(timestamp);
+
+        let (in_phase, quadrature) = lockin.update(
+            adc_signal,
+            demodulation_initial_phase,
+            demodulation_frequency,
+        );
+
+        let magnitude = shift_round(in_phase, 16) * shift_round(in_phase, 16)
+            + shift_round(quadrature, 16) * shift_round(quadrature, 16);
+        let phase = atan2(quadrature, in_phase);
+
+        // Ensure stable within tolerance for 1 time constant after `time_constant_factor`.
+        if n >= samples {
+            // We want our full-scale magnitude to be 1. Our fixed-point numbers treated as integers
+            // set the full-scale magnitude to 1<<60. So, we must divide by this number. However,
+            // we've already divided by 1<<32 in the magnitude computation to keep our values within
+            // the i32 limits, so we just need to divide by an additional 1<<28.
+            let amplitude_normalized =
+                (magnitude as f64 / (1_u64 << 28) as f64).sqrt();
+            assert!(
+                isclose(linear(desired_input.amplitude_dbfs), amplitude_normalized, tolerance, total_magnitude_noise),
+                "magnitude actual: {:.4} ({:.2} dBFS), magnitude computed: {:.4} ({:.2} dBFS), tolerance: {:.4}",
+                linear(desired_input.amplitude_dbfs),
+                desired_input.amplitude_dbfs,
+                amplitude_normalized,
+                dbfs(amplitude_normalized),
+                max_error(linear(desired_input.amplitude_dbfs), amplitude_normalized, tolerance, total_magnitude_noise),
+            );
+            let phase_normalized =
+                phase as f64 / (1_u64 << 32) as f64 * (2. * PI);
+            assert!(
+                isclose(
+                    effective_phase_offset,
+                    phase_normalized,
+                    tolerance,
+                    total_phase_noise
+                ),
+                "phase actual: {:.4}, phase computed: {:.4}, tolerance: {:.4}",
+                effective_phase_offset,
+                phase_normalized,
+                max_error(
+                    effective_phase_offset,
+                    phase_normalized,
+                    tolerance,
+                    total_phase_noise
+                ),
+            );
+
+            let in_phase_normalized = in_phase as f64 / (1 << 30) as f64;
+            let quadrature_normalized = quadrature as f64 / (1 << 30) as f64;
+
+            assert!(
+                isclose(
+                    in_phase_actual,
+                    in_phase_normalized,
+                    total_noise_amplitude,
+                    tolerance
+                ),
+                "in-phase actual: {:.4}, in-phase computed: {:.3}, tolerance: {:.4}",
+                in_phase_actual,
+                in_phase_normalized,
+                max_error(
+                    in_phase_actual,
+                    in_phase_normalized,
+                    total_noise_amplitude,
+                    tolerance
+                ),
+            );
+            assert!(
+                isclose(
+                    quadrature_actual,
+                    quadrature_normalized,
+                    total_noise_amplitude,
+                    tolerance
+                ),
+                "quadrature actual: {:.4}, quadrature computed: {:.4}, tolerance: {:.4}",
+                quadrature_actual,
+                quadrature_normalized,
+                max_error(
+                    quadrature_actual,
+                    quadrature_normalized,
+                    total_noise_amplitude,
+                    tolerance
+                ),
+            );
+        }
+
+        timestamp_start += batch_sample_count;
+    }
+}
+
+#[test]
+fn lowpass() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 100e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 3;
+    let pll_shift_phase: u8 = 2;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 6.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.1 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.9 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_demodulation_phase_offset_pi_2() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 100e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 3;
+    let pll_shift_phase: u8 = 2;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = PI / 2.;
+    let time_constant_factor: f64 = 6.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.1 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.9 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_phase_offset_pi_2() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 100e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 3;
+    let pll_shift_phase: u8 = 2;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 6.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: PI / 2.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.1 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.9 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_fundamental_111e3_phase_offset_pi_4() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 111e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 3;
+    let pll_shift_phase: u8 = 2;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: PI / 4.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.1 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.9 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_first_harmonic() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 50e3;
+    let harmonic: u32 = 2;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_second_harmonic() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 50e3;
+    let harmonic: u32 = 3;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_third_harmonic() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 50e3;
+    let harmonic: u32 = 4;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_first_harmonic_phase_shift() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 50e3;
+    let harmonic: u32 = 2;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: PI / 4.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_adc_frequency_1e6() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 32.;
+    let signal_frequency: f64 = 100e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_internal_frequency_125e6() {
+    let internal_frequency: f64 = 125e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 100e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-2;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![
+            PureSine {
+                frequency: 1.2 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+            PureSine {
+                frequency: 0.8 * demodulation_frequency,
+                amplitude_dbfs: -20.,
+                phase_offset: 0.,
+            },
+        ],
+        time_constant_factor,
+        tolerance,
+    );
+}
+
+#[test]
+fn lowpass_low_signal_frequency() {
+    let internal_frequency: f64 = 100e6;
+    let adc_frequency: f64 = internal_frequency / 64.;
+    let signal_frequency: f64 = 10e3;
+    let harmonic: u32 = 1;
+    let sample_buffer_size_log2: usize = 2;
+    let pll_shift_frequency: u8 = 2;
+    let pll_shift_phase: u8 = 1;
+    let corner_frequency: f64 = 1e3;
+    let demodulation_frequency: f64 = harmonic as f64 * signal_frequency;
+    let demodulation_phase_offset: f64 = 0.;
+    let time_constant_factor: f64 = 5.;
+    let tolerance: f64 = 1e-1;
+
+    lowpass_test(
+        internal_frequency,
+        adc_frequency,
+        signal_frequency,
+        demodulation_phase_offset,
+        harmonic,
+        sample_buffer_size_log2,
+        pll_shift_frequency,
+        pll_shift_phase,
+        corner_frequency,
+        PureSine {
+            frequency: demodulation_frequency,
+            amplitude_dbfs: -30.,
+            phase_offset: 0.,
+        },
+        &mut vec![PureSine {
+            frequency: 1.1 * demodulation_frequency,
+            amplitude_dbfs: -20.,
+            phase_offset: 0.,
+        }],
+        time_constant_factor,
+        tolerance,
+    );
+}