Modified Mean Frequency (MMNF)

• Modified Mean Frequency (MMNF) is a spectral-domain feature that computes the mean frequency using the amplitude spectrum to enhance noise robustness in EMG analysis.
• It replaces the traditional power spectrum with the amplitude spectrum, reducing noise-induced estimation errors and simplifying real-time processing.
• MMNF has shown lower percentage errors and improved classification performance under various SNRs, making it valuable for prosthetic control and EMG-based pattern recognition.

Modified Mean Frequency (MMNF) is a spectral-domain feature introduced for noise-tolerant electromyography (EMG) pattern recognition. Designed to increase robustness to white Gaussian noise (WGN), MMNF redefines the classical mean frequency calculation using the amplitude spectrum instead of the power spectrum. This modification significantly reduces noise-induced estimation error, particularly under low signal-to-noise ratio (SNR) conditions relevant to EMG acquisition for prosthetic control and pattern recognition (0912.3973).

1. Formal Definition and Algorithm

Let $x[n]$, $n=0,\dots,N-1$, be a single window of the band-pass filtered EMG signal. Compute its discrete Fourier transform: $$X[k]=\sum_{n=0}^{N-1}x[n]\,e^{-j2\pi kn/N},\quad k=0,\dots,N-1$$ Construct the one-sided amplitude spectrum: $$A_j=|X[j]|,\quad j=0,1,\dots,M,\ \ M= \lfloor N/2 \rfloor$$ The Modified Mean Frequency is then defined as the mean frequency calculated with the amplitude (not power) spectrum: $$\mathrm{MMNF} = \frac{\sum_{j=0}^{M} f_j\,A_j}{\sum_{j=0}^{M}A_j}$$ where $f_j = \frac{j}{N} F_s$ gives frequency in Hz at bin $j$ for sampling frequency $F_s$.

Pseudocode

$n=0,\dots,N-1$3 Window size ($N=W=256$) and overlap ($O=64$) as per experimental protocol (0912.3973).

2. Motivation and Comparison to Classical Mean Frequency

Traditional mean frequency (MNF) is derived from the power spectrum $n=0,\dots,N-1$0. The modified approach replaces $n=0,\dots,N-1$1 by $n=0,\dots,N-1$2 in both numerator and denominator, reducing the amplification of artifacts from high-power spectral bins, which tend to be exaggerated under noise or strong motor unit action potentials (MUAPs). This substitution reduces estimator variance and increases noise robustness, specifically when contaminated by WGN, as amplitude reacts linearly rather than quadratically to random perturbations.

3. Robustness Under Noisy Conditions

MMNF explicitly targets improved tolerance to WGN without relying on dedicated noise-removal algorithms (e.g., wavelets, adaptive filters). Quantitative evaluation involved corrupting clean forearm EMG signals with controlled levels of WGN to achieve SNRs of 20, 15, 10, 5, and 0 dB. For weak EMG at 0 dB, the MMNF error was approximately 5–10%, contrasted with >20% for classical mean frequency and most standard features (0912.3973). In strong EMG, MMNF consistently achieved lower error rates than all alternative features across all SNRs tested.

SNR (dB)	20	15	10	5	0
Weak EMG PE	~5%	~7%	~8%	~9%	10%
Strong EMG PE	~2%	~3%	~4%	~6%	~6%

PE = percentage error of MMNF on noisy vs. clean signal, estimated from data (0912.3973).

4. EMG Acquisition and Experimental Protocol

EMG was recorded from the forearm using 8 surface electrode channels. Signals underwent hardware band-pass filtering (10–500 Hz, gain 60 dB) and digital sampling at either 1 kHz directly or 3 kHz (downsampled to 1 kHz). Windows of length 256 ms with 64 ms overlap were subjected to the feature-extraction pipeline. Evaluated gestures included wrist flexion/extension, hand open/close (for error metrics), and a larger set for classification experiments.

5. Classification Performance and Feature Combinations

For pattern recognition, various feature vectors were constructed using time- and frequency-domain features, including MMNF, Willison amplitude (WAMP), and histogram bins (HEMG). Linear discriminant analysis (LDA) with majority voting over windows was employed. The combination {MMNF, HEMG, WAMP} outperformed all single features and most alternative multi-feature sets, particularly as noise increased. The below table summarizes representative LDA classification rates at various SNRs:

Feature Set	Clean	20 dB	15 dB	10 dB
MMNF	41.1	36.4	32.7	17.1
HEMG+WAMP+MMNF	93.1	96.2	64.1	28.1

This suggests that MMNF contributes substantial robustness to feature vectors under adverse noise conditions, making it suitable for practical prosthetic or real-time myoelectric applications.

6. Strengths, Limitations, and Use Cases

Key advantages of MMNF include the elimination of explicit noise-removal steps before feature extraction, computational simplicity (one FFT and a weighted sum per window), and combined immunity to broad-band WGN (PE < 6% at 0 dB SNR). MMNF is easily integrated with established time-domain features for improved pattern recognition, especially when SNR cannot be controlled. The primary limitation is performance degradation below 5 dB SNR (PE 7–10%), and absence of higher-order spectral sensitivity. Recommended use cases are real-time prosthetic myoelectric control and all EMG classification pipelines where broad-band interference is present and not easily filtered (0912.3973).

7. Summary and Outlook

MMNF provides a low-cost, effective, and noise-robust modification to frequency-domain feature extraction from EMG signals. By leveraging amplitude spectrum statistics rather than power, MMNF achieves greater stability in the presence of additive wide-band noise, and enables reliable pattern recognition even under challenging SNR regimes. These properties make MMNF a practical drop-in replacement for classical mean frequency features in robust EMG-based control and recognition systems (0912.3973).