Histogram of EMG: Noise-Resilient Feature

• Histogram of EMG is a time-domain feature that discretizes sEMG signals into equally spaced amplitude bins to quantify the signal's distribution.
• Its three-bin strategy, particularly using the middle bin, yields enhanced noise tolerance compared to traditional EMG features under white Gaussian noise.
• HEMG is pivotal in robust EMG pattern recognition, especially when fused with features like MMNF and WAMP, enhancing classification accuracy in low SNR conditions.

The Histogram of EMG (HEMG) is a time-domain feature that quantifies the distribution of sample amplitudes in surface electromyography (sEMG) signals by partitioning each analysis window into equally spaced bins and counting the occurrences in each bin. Introduced as part of a comparative study on robust EMG pattern recognition, HEMG has demonstrated substantial noise tolerance under conditions of white Gaussian noise (WGN), particularly when constructed with a three-segment binning strategy and reduced to the second bin as the feature of interest (0912.3973).

1. Mathematical Construction and Definition

HEMG is mathematically defined by discretizing an EMG signal segment of length $N$ into $B$ amplitude bins spanning the minimum ($L$) to the maximum ($U$) values observed in the segment. The count in the $j$-th bin, $h_j$, is computed as

$$\mathrm{HEMG}_j = \sum_{n=1}^{N} \mathbf{1}\Bigl( x(n) \in \bigl[L + (j-1)\Delta,\, L + j\,\Delta\bigr) \Bigr),$$

where

$$\Delta = \frac{U - L}{B}, \quad L = \min_n x(n), \quad U = \max_n x(n), \quad 1 \leq j \leq B,$$

and $\mathbf{1}(\cdot)$ is the indicator function.

No normalization or scaling is applied to the bin counts; $h_j$ is a raw count of signal samples falling within the prescribed amplitude interval [(0912.3973), section 3.1.13].

2. Binning Strategies and Feature Selection

The original investigation evaluated five bin counts ($B$0): 3, 5, 7, 9, and 11. All binning strategies partition the observed range $B$1 into equally spaced intervals. Performance evaluation across various signal-to-noise ratio (SNR) regimes indicated that the single most noise-tolerant implementation utilized $B$2 and extracted only the count of the second (middle) bin as the feature for all subsequent analysis. This practice was empirically justified by percent-error (PE) measurements, which consistently favored this configuration under all tested noise conditions. A plausible implication is that intermediate bins are less sensitive to outlier excursions induced by noise, capturing central tendencies more robustly [(0912.3973), Fig. 6(e)].

3. Signal Acquisition and Pre-processing

The analog front end applies a 10–500 Hz band-pass filter with 60 dB gain. Signals are digitized at 1 kHz/3 kHz (down-sampled to 1 kHz for feature extraction). HEMG (and comparators) are computed on either non-overlapping or sliding windows, each comprising 256 ms (256 samples at 1 kHz), with a sliding step of 64 ms for classification tasks. No explicit noise filtering or denoising is performed; white Gaussian noise is left unmitigated to directly assess feature robustness. This ensures that all computed features, including HEMG, are directly sensitive to the combined effect of physiological and instrumentation noise.

4. Noise Robustness and Quantitative Performance

The robustness of HEMG was substantiated by adding zero-mean white Gaussian noise to clean sEMG signals, with total SNRs set to 20, 15, 10, 5, and 0 dB. The percentage error (PE) between noisy and clean features is defined as

$B$3

Empirical results indicate the following PE values for HEMG (second bin of $B$4) [(0912.3973), Fig. 7]:

Condition	SNR (dB)	Strong EMG PE (%)	Weak EMG PE (%)
Low noise	20	1–2	3–5
Moderate noise	10	6–8	12–15
Maximum noise	0	12–15	18–20

For comparison, traditional features such as RMS, AR₁, MNF, and MDF exhibit PE values exceeding 20–30% as SNR drops below 10 dB. This demonstrates that HEMG, specifically as the count in the second of three bins, offers comparatively strong resistance to additive WGN, though the modified mean frequency (MMNF) feature outperforms it in the lowest SNR regimes.

5. Classification Performance and Feature Fusion

Classification tasks leveraged features extracted from eight EMG channels, using linear discriminant analysis (LDA) followed by majority-vote postprocessing. For single-feature HEMG (second of three bins, per channel), observed classification accuracies were:

SNR (dB)	Accuracy (%)
Clean	60.78
20	49.16
15	41.79
10	34.68

When HEMG was fused with two additional robust features—MMNF and Willison amplitude (WAMP, 10 mV threshold)—to form a 3-feature vector per channel (24-dimensional overall), classification performance improved substantially:

SNR (dB)	MMNF+WAMP+HEMG (%)	Hudgins (%)	RMS+AR₂ (%)
Clean	93.08	95.68	96.49
20	96.19	67.43	89.89
15	64.06	22.57	64.87
10	28.12	7.98	25.27

In high-noise conditions, this composite set outperformed both Hudgins’ (MAV, WL, ZC, SSC) and Oskoei & Hu’s (RMS, AR₂) feature sets, which suffered a pronounced accuracy collapse at SNR < 15 dB.

6. Applications and Implications in Robust EMG Pattern Recognition

HEMG’s principal value lies in robust feature extraction for EMG-based pattern recognition under non-ideal (noisy) acquisition conditions. Its low sensitivity to WGN, especially when operationalized as a single bin-count in coarse (three-bin) histograms, makes it suitable for real-time prosthetic control and other scenarios where preprocessing cannot fully ameliorate noise artifacts. Its integration with MMNF and WAMP, both individually noise-tolerant, facilitates feature sets that preserve discrimination power under extreme SNR degradation.

7. Concluding Remarks and Limitations

HEMG, as formalized (bin count of the center segment with $B$5), provides a compact, noise-resilient time-domain descriptor. Its performance, both as a single feature and as part of a fused set, highlights the utility of amplitude-distribution-based measures in sEMG feature engineering. A plausible implication is that simple, histogram-based features can outperform more sophisticated time-frequency features when the measurement context is constrained by non-removable WGN and when computational simplicity is advantageous (0912.3973). However, MMNF remains superior in absolute noise robustness, and HEMG’s effectiveness is conditional on appropriately selected windowing and binning strategies.