Time-Interleaved ADC Analysis (timeinterleave)#

The timeinterleave module provides utilities for channel splitting, mismatch extraction, spur prediction, and foreground correction in time-interleaved ADCs.

Data Layout#

adctoolbox.deinterleave(x: ndarray, M: int) → ndarray[源代码]#

Deinterleave x into M sub-channels.

参数:

  • x (array_like, shape (N,)) -- Interleaved time series. Sample at index n belongs to channel n mod M.

  • M (int) -- Number of sub-ADCs (channels).

返回:

channels -- channels[m] contains the samples of channel m in chronological order.

返回类型:

ndarray, shape (M, N // M)

adctoolbox.interleave(channels: ndarray) → ndarray[源代码]#

Inverse of deinterleave() — stitch M channels back into one stream.

参数:

channels (array_like, shape (M, K)) -- channels[m, k] is the k-th sample of channel m.

返回:

x

返回类型:

ndarray, shape (M * K,)

Mismatch Analysis#

adctoolbox.extract_mismatch_sine(x: ndarray, M: int, fs: float, fin: float | None = None) → dict[源代码]#

Extract per-channel offset, gain, and sample-skew from a TI-ADC sine capture.

参数:

  • x (array_like, shape (N,)) -- Interleaved output. Sample x[n] belongs to channel n mod M and was taken at time n / fs.

  • M (int) -- Number of sub-ADCs.

  • fs (float) -- Aggregate sample rate (Hz).

  • fin (float, optional) -- Input-tone frequency. If None, it is estimated from the FFT of x (use coherent sampling for best results).

返回:

params -- gain : (M,) relative gain, normalized so mean == 1. offset : (M,) DC offset per channel (same units as x). skew : (M,) sample-skew per channel (seconds, mean zero). fin : float — tone frequency used for the fit. A : float — fitted fundamental amplitude (mean across channels). phases : (M,) raw fitted phase per channel (rad) for diagnostics.

返回类型:

dict

备注

The "skew" returned here is relative: the mean is subtracted so an overall clock delay (which is not observable from a single capture) does not leak into the per-channel result. Pass skew - skew.mean() upstream.

adctoolbox.predict_spurs(params: dict, fs: float, fin: float | None = None, full_scale: float = 1.0) → list[dict][源代码]#

Predict TI-ADC spur frequencies and magnitudes.

参数:

  • params (dict) -- Output of extract_mismatch_sine(). Must contain gain, offset, skew, and at least one of fin / A; fin can also be supplied via the argument below.

  • fs (float) -- Aggregate sample rate (Hz).

  • fin (float, optional) -- Input-tone frequency. Defaults to params['fin'] if present.

  • full_scale (float, default 1.0) -- Signal full-scale (peak) used as the dBFS reference. If your x was scaled so the ideal sine has peak amplitude A, set full_scale = A_full_scale — usually the converter's peak code.

返回:

spurs -- One dict per predicted spur with keys:

  • freq_hz : spur frequency folded to [0, fs/2]

  • kind : 'offset' or 'gain_skew'

  • k : spur index in the M-point DFT (1..M-1)

  • amp : spur amplitude in the same units as x

  • dbfs : spur magnitude in dBFS (relative to full_scale)

  • dbc : spur magnitude in dBc (relative to fundamental)

返回类型:

list of dict

Correction#

adctoolbox.fractional_delay_fft(x: ndarray, delay_sec: float, fs: float) → ndarray[源代码]#

Apply a fractional-sample delay via DFT phase rotation.

Output y[n] approximates x((n / fs) - delay_sec) using the sinc interpolation implicit in a length-N DFT. Exact for signals that are periodic over their length and strictly bandlimited to [0, fs/2).

参数:

  • x (array_like, 1-D real)

  • delay_sec (float) -- Delay in seconds; positive = later in time, negative = earlier.

  • fs (float) -- Sample rate (Hz).

返回:

y

返回类型:

ndarray, same length as x.

备注

Because the DFT assumes periodic extension, non-periodic signals will wrap around when |delay_sec| approaches the full record length. For clean results near the edges, zero-pad x before calling and trim afterwards.

adctoolbox.fractional_delay_farrow(x: ndarray, delay_sec: float, fs: float, n_taps: int = 7) → ndarray[源代码]#

Apply a fractional-sample delay via a Lagrange FIR interpolator.

Causal / streaming alternative to fractional_delay_fft(). The n_taps-tap centered filter trades accuracy against boundary transient length (n_taps // 2 samples on each end are unreliable, because the same-mode convolution zero-pads the input edges).

参数:

  • x (array_like, 1-D real)

  • delay_sec (float)

  • fs (float)

  • n_taps (int, default 7) -- Must be a positive odd integer. 5–9 is typical; higher = flatter passband but longer transient.

返回:

y

返回类型:

ndarray, same length as x.

备注

The delay is split into an integer part (applied by zero-padded shift) and a fractional remainder in (-0.5, 0.5] handled by the centered Lagrange filter. When delay_sec == 0 the filter is an impulse at the center tap.

adctoolbox.calibrate_foreground(x: ndarray, M: int, params: dict, fs: float, *, skew_method: str = 'fft', n_taps: int = 7) → ndarray[源代码]#

Apply offset / gain / skew corrections to a TI-ADC interleaved capture.

参数:

  • x (array_like, shape (N,)) -- Interleaved time series.

  • M (int) -- Sub-ADC count.

  • params (dict) -- Output of extract_mismatch_sine(). Required keys: offset, gain, skew.

  • fs (float) -- Aggregate sample rate (Hz).

  • skew_method ({'fft', 'farrow'}, default 'fft') --

    How to apply the fractional-sample skew correction:

    • 'fft' — per-channel DFT phase rotation. Near machine-precision accuracy for signals with energy strictly below fs/(2M); circular wrap at record boundaries.

    • 'farrow' — per-channel Lagrange FIR. Causal and streaming-friendly. Accuracy and boundary transient length are set by n_taps.

  • n_taps (int, default 7) -- Only consulted when skew_method == 'farrow'; must be a positive odd integer.

返回:

y -- Calibrated interleaved signal.

返回类型:

ndarray, shape (N,)

备注

The order matters: offset is removed first (before gain normalization), then gain is applied, and skew correction is last — mixing channels only at the fractional-delay interpolation stage preserves the per-channel amplitude balance that the prior two steps just enforced.