Signal Segmentation and framing

Department of Data Communication Networks and Systems

Lecturer Shukhrat Palvanov

�Signal framing is a fundamental technique in digital signal processing (DSP) used to divide a continuous-time or discrete-time signal into smaller segments called frames.�Each frame represents a short segment of time where the signal is assumed to be quasi-stationary (its properties remain almost constant).�This segmentation allows analysis of time-varying signals, such as speech, music, or biomedical signals, using short-time analysis techniques.�Instead of processing the entire signal at once, framing enables frame-by-frame processing, which provides both time-domain and frequency-domain insights.�For example, in speech processing, human speech changes continuously as we talk. By framing the signal into small intervals (e.g., 20–40 milliseconds), we can extract useful information such as pitch, energy, and formant frequencies for each short period.�

Introduction to Signal Framing

Why Signal Framing is Needed�

• Most real-world signals, such as speech, audio, and biomedical signals, are non-stationary, meaning their properties (amplitude, frequency, phase) change over time.
• Many signal processing algorithms (e.g., Fourier Transform, spectral analysis) assume that the signal is stationary, i.e., its characteristics do not change during analysis.
• To apply these methods effectively, the signal must be divided into small time intervals where it can be considered approximately stationary.
• This is achieved through framing, which allows localized analysis of the signal in both time and frequency domains.

Key Benefits of Signal Framing�

• Enables short-time analysis of long signals.
• Makes feature extraction (e.g., energy, zero-crossing rate, pitch, spectral coefficients) more accurate.
• Allows better pattern recognition in applications like speech or emotion detection.
• Reduces computational complexity by processing smaller segments instead of the entire signal at once.
• Provides temporal resolution, helping to identify how signal characteristics evolve over time.

How Framing Works�

1. A continuous signal x(t)x(t)x(t) or discrete signal x[n]x[n]x[n] is divided into segments of equal length.
2. Each segment (frame) contains a fixed number of samples, typically between 256 and 1024 samples, depending on the application.
3. Frames may overlap partially to maintain smooth transitions between consecutive frames and to avoid losing information at boundaries.
4. The degree of overlap usually ranges between 25% and 50% of the frame size.

Frame Size and Overlap�

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Frame Size (N): The number of samples contained in each frame.

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Frame Shift (M): The number of samples between the starting points of two consecutive frames.

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Overlap: The portion of the signal shared by adjacent frames, calculated as:

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Overlap=N−M

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Importance of Choosing Proper Frame Size

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The frame size determines the time and frequency resolution of the analysis.

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A smaller frame size provides better time resolution but poorer frequency resolution.

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A larger frame size improves frequency resolution but may lose short-time variations.

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The choice depends on the signal type and the goal of analysis.

Example Calculation�

• Sampling rate: 16 kHz
• Frame size: 25 ms → 0.025×16000=400 samples
• Frame shift: 10 ms → 0.010×16000=160 samples
• Overlap: 400−160=240 samples (≈ 60%)

This means each new frame starts 160 samples after the previous one, with 240 samples overlapping.

Mathematical Representation of Framing

The framing process can be described mathematically to formalize how a continuous signal is divided into short, fixed-length segments.

Example of Signal Framing

Given Signal Parameters

• Signal type: Recorded speech sample
• Duration: 1 second
• Sampling rate: 16 kHz → 16,000 samples per second
• Frame size: 25 ms → 0.025×16000=400 samples
• Frame shift: 10 ms → 0.010×16000=160 samples
• Overlap: 400−160=240 samples (≈ 60%)

Summary

Signal framing is the process of dividing a long, continuous signal into short, fixed-size segments (frames) to facilitate analysis.

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This technique assumes that within each frame, the signal is approximately stationary, allowing the use of various DSP methods such as FFT, filtering, or feature extraction.

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Framing is often combined with windowing to reduce edge discontinuities and minimize spectral leakage.