Expert Insights into Waveform Analysis Techniques

Update 10/28: Please find here the Installation Guide for the tools that you can optionally install if you want to be able to run the example files

Are you capturing real-world waveforms and striving for pinpoint accuracy in your measurements? Whether you're working with single tones, broadband noise, or arbitrary waveforms in the analog or digital domain, this workshop is designed for you!

Explore advanced but user-friendly frequency and time domain methods applicable to the assessment of signal to noise ratios and EVM (error vector magnitude) for communications waveforms, number of effective bits in A/D conversion, or any application where an accurate measurement of noise is critical.

Learn from a seasoned expert the industry-leading techniques that push the boundaries of traditional test set-ups. The workshop will feature practical “cookbook” techniques using Python (with similar methods in MATLAB and Octave) and provide in-depth insights into both the effective use and potential pitfalls of these methods.

In this engaging session, you will:

• Master FFT-based techniques for single tone measurements of any frequency without any concern for scalloping loss.
• Extend the accurate measurement of single tones to multi-tones and broadband arbitrary waveforms.
• Achieve sub-dB precision in broadband noise density measurements.
• Optimize signal capture duration using the Allan Deviation statistical tool.

Don't miss this opportunity to refine your measurement skills and overcome common limitations. Whether you're a seasoned professional or new to the field, you'll leave with actionable insights and hands-on techniques to elevate your waveform measurement capabilities.

What this presentation is about and why it matters

This talk presents practical, high-precision methods for analyzing real-world waveforms in both the time and frequency domains. It focuses on measuring tones, broadband noise, and arbitrary modulated signals (for example QAM) with accuracy sufficient for tasks like ENOB (effective number of bits) estimation, noise-density measurements, EVM/SNR assessment, and diagnosing non-stationary behavior. The speaker emphasizes methods you can run in post-processing (Python/MATLAB/Octave), and shows how to avoid common pitfalls that produce dB-level errors.

Who will benefit the most from this presentation

• RF and mixed-signal engineers validating ADCs, receivers, or front-end chains.
• DSP engineers and researchers who analyze captured waveforms and need reliable SNR / noise-floor metrics.
• Test and measurement engineers who want cookbook procedures for FFT, Welch PSD, EVM, and Allan deviation.
• Students learning practical spectrum analysis and waveform-quality metrics.

What you need to know

Before watching, a basic familiarity with these concepts will help you get the most from the talk. The presenter demonstrates concrete recipes, but understanding the background will make the examples clearer.

• Sampling and Nyquist — sampling rate Fs, bin spacing Fs/N, and why capture duration sets frequency resolution.
• FFT basics — the FFT/DFT produces a bank-of-filters view of the spectrum. You should know what a bin represents (frequency and resolution). Zero-padding changes the interpolation of the spectrum but not intrinsic resolution.
• Windowing and spectral leakage — time-domain windows (e.g., Kaiser, Hann, rectangular) trade main-lobe width (resolution bandwidth) for sidelobe attenuation (reduced leakage). Scaling the FFT by the sum of window coefficients corrects amplitude loss.
• Scalloping loss & zero-padding — peak amplitude varies with tone position relative to bin centers; zero-padding plus windowing reduces scalloping loss significantly.
• Power spectral density (PSD) and Welch method — Welch averages power spectra of overlapping, windowed blocks to estimate noise density (dB/Hz). Key knobs: block size, overlap, window type, and averaging (mean vs median).
• EVM and correlation — EVM is the RMS error between measured samples and ideal reference; when scaled properly SNR ≈ 1 / EVM^2. Correlation (complex cross-correlation) between measurement and template gives |r| and SNR via the power formula SNR = |r|^2/(1-|r|^2). Remove mean, normalize by standard deviation, and correct time/frequency/phase offsets first.
• ENOB and quantization — the classical SNR formula for an ideal N-bit ADC: \(\mathrm{SNR_{dB}} \approx 6.02\,N + 1.76\,\mathrm{dB}\). Use PSD (dBFS/Hz) plus bandwidth integration to compute total noise power and confirm SNR/ENOB.
• Non-stationarity and Allan deviation — long captures may include drift and low-frequency noise (1/f, random walk). Allan deviation (two-sample) quantifies stability vs averaging time and helps choose an optimal capture duration for stationary estimates.
• Practical alignment tips — accurate time alignment (sub-sample) is critical for EVM; polyphase resampling or a fractional-delay filter bank can provide sub-sample shifts. Remove DC/mean, correct phase/frequency offsets, and normalize amplitudes before metric calculation.

Glossary (terms used in this talk)

• FFT (Fast Fourier Transform): An efficient algorithm for computing the discrete Fourier transform.
• EVM (Error Vector Magnitude): A normalized measure of modulation error defined from the difference between ideal and received symbols; it reflects the combined impact of noise, distortion, imbalance, and offsets.
• Resolution Bandwidth (RBW): The frequency spacing between adjacent spectral estimates or FFT bins; it sets the smallest frequency separation that can be distinguished in a spectrum display or estimate.
• Window (e.g., Blackman): A taper applied to each frame to reduce spectral leakage before computing the FFT.
• Scalloping loss: Amplitude error that occurs when a tone does not fall exactly at the center of a frequency-analysis bin.
• Welch PSD: A power spectral density estimation method that averages periodograms from overlapping, windowed data segments to reduce variance.
• Correlation coefficient: A normalized measure of similarity between two signals, often computed as a complex inner product in waveform analysis.
• ENOB (Effective Number of Bits): A metric that expresses an ADC's effective resolution based on measured signal-to-noise performance.

Final thoughts

This overview is AI-generated from the session transcript. Spot an issue? Let us know.