analyze_error_spectrum

Overview

analyze_error_spectrum computes the FFT spectrum of the ADC error signal (data - fitted sine) to reveal frequency components in the error. This is distinct from analyzing the signal spectrum itself—here we analyze only the residual error after removing the ideal sine wave.

Syntax

from adctoolbox import analyze_error_spectrum

# Basic usage
result = analyze_error_spectrum(signal, fs=100e6, show_plot=True)

# With known frequency
result = analyze_error_spectrum(signal, fs=800e6, frequency=0.123,
                                show_plot=True)

# Custom title
result = analyze_error_spectrum(signal, fs=100e6, show_plot=True,
                                title="Error Spectrum: 25°C")

Parameters

signal (array_like) — Input ADC signal (sine wave excitation)
fs (float, default=1) — Sampling frequency in Hz
frequency (float, optional) — Normalized frequency (0-0.5)
- If None: auto-detected via FFT
show_plot (bool, default=True) — Display error spectrum plot
ax (matplotlib axis, optional) — Axis to plot on
title (str, optional) — Title for the plot

Returns

Dictionary containing:

Metrics (of error signal):

enob — Effective Number of Bits
sndr_db — Signal-to-Noise and Distortion Ratio (dB)
sfdr_db — Spurious-Free Dynamic Range (dB)
snr_db — Signal-to-Noise Ratio (dB)
thd_db — Total Harmonic Distortion (dB)
sig_pwr_dbfs — Signal power (dBFS)
noise_floor_dbfs — Noise floor (dBFS)

Error Data:

error_signal — Error signal (data - fitted sine)

Algorithm

# 1. Fit ideal sine wave
if frequency is None:
    result = fit_sine_4param(signal)
else:
    result = fit_sine_4param(signal, frequency_estimate=frequency)

fitted_sine = result['fitted_signal']

# 2. Compute error
error_signal = signal - fitted_sine

# 3. Analyze spectrum of error (not signal!)
spectrum_result = analyze_spectrum(error_signal, fs=fs)

Key Difference from analyze_spectrum

Function	What it Analyzes	Use Case
`analyze_spectrum`	Original signal spectrum	Overall ADC performance (ENOB, SNR, harmonics)
`analyze_error_spectrum`	Error signal spectrum	Error characteristics, frequency-dependent errors

Examples

Example 1: Error Spectrum Analysis

import numpy as np
from adctoolbox import analyze_error_spectrum

# Analyze error spectrum
result = analyze_error_spectrum(adc_signal, fs=800e6, show_plot=True)

print(f"Error SNDR: {result['sndr_db']:.2f} dB")
print(f"Error SFDR: {result['sfdr_db']:.2f} dB")
print(f"Noise floor: {result['noise_floor_dbfs']:.2f} dBFS")

Example 2: Compare Signal vs. Error Spectra

import matplotlib.pyplot as plt
from adctoolbox import analyze_spectrum, analyze_error_spectrum

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))

# Signal spectrum (shows fundamental + harmonics + noise)
plt.sca(ax1)
sig_result = analyze_spectrum(signal, fs=fs, show_plot=True)
ax1.set_title('Signal Spectrum')

# Error spectrum (shows harmonics + noise, NO fundamental)
plt.sca(ax2)
err_result = analyze_error_spectrum(signal, fs=fs, show_plot=True)
ax2.set_title('Error Spectrum')

plt.tight_layout()
plt.show()

Example 3: Identify Frequency-Dependent Errors

# Look for spurs in error spectrum
result = analyze_error_spectrum(signal, fs=800e6, show_plot=True)

# Error spectrum should be relatively flat (white noise)
# Peaks indicate frequency-dependent errors:
# - Power supply coupling
# - Clock feedthrough
# - Sampling artifacts

Example 4: Batch Analysis

# Analyze multiple conditions
conditions = ['Room Temp', 'High Temp', 'Low Voltage']
signals = [sig_25c, sig_85c, sig_low_vdd]

for cond, sig in zip(conditions, signals):
    result = analyze_error_spectrum(sig, fs=fs, show_plot=False,
                                     title=cond)
    print(f"{cond:15s}: Error SNDR = {result['sndr_db']:.2f} dB")

Interpretation

Error Spectrum Shape

Spectrum Shape	Interpretation
Flat (white)	Random noise (thermal, quantization)
1/f shape	Flicker noise, drift
Peaks at harmonics	Nonlinearity (HD2, HD3, etc.)
Peaks at non-harmonics	Spurs (power supply, clock coupling)
High at low freq	Offset drift, 1/f noise

Common Error Signatures

Peak Location	Likely Cause
DC (0 Hz)	Offset drift (should be minimal)
f_clock	Clock feedthrough
f_supply	Power supply ripple
2×f_in, 3×f_in	Harmonic distortion
f_in ± f_clock	Sampling artifacts

SFDR of Error

Error SFDR > 80 dB: Excellent, noise-limited
60 < Error SFDR < 80 dB: Good, some distortion
Error SFDR < 60 dB: Significant spurious content

Use Cases

Distinguish noise from distortion in error
Identify interference sources (spurs in error spectrum)
Validate fitting quality (DC component should be near zero)
Debug frequency-dependent errors
Measure noise floor excluding signal energy

Comparison with Other Error Analysis

Function	Domain	Shows
`analyze_error_spectrum`	Frequency	Error frequency components
`analyze_error_pdf`	Statistical	Error distribution
`analyze_error_autocorr`	Time	Temporal correlation
`analyze_error_envelope_spectrum`	Frequency	AM modulation in error
`analyze_error_by_phase`	Phase	AM/PM decomposition

References

IEEE Std 1241-2010, “IEEE Standard for Terminology and Test Methods for ADCs”
B. Razavi, “Principles of Data Conversion System Design,” IEEE Press, 1995