The Hamming window is closely related to the Hann window and is one of the most commonly used window functions in Digital Signal Processing. It has a similar smooth shape, but unlike the Hann window, it does not go exactly to zero at the edges. Instead, it introduces a small non-zero offset that improves its spectral characteristics, particularly in terms of side lobe suppression. This makes it especially useful when minimizing interference from nearby frequency components is more important than perfect edge tapering.
Time-Domain Effect: The original signal (gray) continues with full amplitude to the edges, while the Hamming-windowed signal (blue) is tapered but does not reach exactly zero at the boundaries, leaving a small discontinuity.
Frequency-Domain Comparison: The rectangular window (red) shows strong spectral leakage, with side lobes only 15–30 dB below the main peak. The Hamming window (blue) suppresses the first side lobe to approximately -41 dB, significantly reducing nearby spectral leakage.
This small adjustment in the coefficients changes the fundamental trade-off between time-domain behavior and frequency-domain performance. By not forcing the window to zero at the boundaries, the Hamming window reduces the amplitude of the first side lobe in the frequency spectrum more effectively than the Hann window. The first side lobe of the Hamming window is attenuated to about -41 dB, compared to approximately -31 dB for the Hann window.
Use Case: Speech Processing and Formant Analysis
In speech processing, the Hamming window is the traditional choice for formant analysis and spectrogram generation. When analyzing voiced speech sounds (vowels), the harmonics are spaced by the fundamental frequency (typically 80–300 Hz). The superior first side lobe suppression of the Hamming window helps distinguish these harmonics from spectral leakage, making formant frequencies (resonances of the vocal tract) more clearly visible.
Practical example: In the classic "Linear Predictive Coding (LPC)" analysis for speech coding and recognition, Hamming windowing is applied before autocorrelation computation. The reduced spectral leakage from nearby harmonics improves the stability and accuracy of the resulting LPC coefficients, leading to better speech synthesis and recognition performance.
Trade-offs and Limitations
The trade-off is slightly worse behavior at the boundaries compared to the Hann window. Because the Hamming window does not fully reach zero (its endpoints are at approximately 0.08 instead of 0), there is a small residual discontinuity when the signal is periodically extended in the context of the DFT. This results in slightly higher far side lobes (far from the main peak) compared to the Hann window. However, for most practical applications where nearby frequency components are the primary concern, this is an acceptable compromise.
Compared to the Hann window, the Hamming window can therefore be seen as a more "frequency-optimized" design, while the Hann window is more "time-domain smoothness optimized." Both are widely used, and the choice between them depends on whether edge continuity or first side lobe suppression is more critical for the application.
Conclusion
The Hamming window is best suited for applications where minimizing interference from nearby frequency components is critical, such as speech processing, formant analysis, and spectral estimation. Its first side lobe is attenuated to -41 dB (compared to -31 dB for Hann), making it superior for distinguishing closely spaced spectral components. However, it leaves a small discontinuity at the boundaries (endpoints ≈ 0.08), resulting in slightly higher far side lobes. For most speech and audio applications, this trade-off is well worth the improved spectral clarity.
See also: Implementation guide for Hamming window