Spectral Analysis Tool

Spectral analysis examines the frequency content of signals. It reveals which frequencies are present and how strong they are, helping to identify periodic patterns, harmonics, and noise characteristics.

Key concepts:

• FFT (Fast Fourier Transform): Efficiently converts time-domain signals to frequency domain
• Frequency Spectrum: Shows the amplitude or power of each frequency component
• Spectrogram: Displays how the spectrum changes over time

Window functions reduce spectral leakage when analyzing finite signal segments:

• Rectangular: No windowing. Best frequency resolution but highest spectral leakage
• Hanning: Good general-purpose window. Smooth transition to zero at edges
• Hamming: Similar to Hanning but slightly different shape. Slightly higher sidelobes
• Blackman: Excellent sidelobe suppression but wider main lobe
• Bartlett: Triangular window. Simple but less effective than Hanning

The spectrogram is a time-frequency representation created by:

1. Dividing the signal into overlapping segments
2. Applying a window function to each segment
3. Computing the FFT of each windowed segment
4. Displaying the magnitude as a color-coded image

Parameters:

• FFT Size: Larger sizes give better frequency resolution but worse time resolution
• Overlap: Higher overlap gives smoother spectrograms but requires more computation

• Single Sine Wave: Pure tone at one frequency. Spectrum shows a single peak
• Multiple Frequencies: Sum of several sine waves. Spectrum shows multiple peaks
• Chirp: Frequency sweep from low to high. Spectrogram shows rising frequency over time
• White Noise: Random signal with equal power at all frequencies. Flat spectrum

• Audio Processing: Music analysis, speech recognition, audio effects
• Vibration Analysis: Machine condition monitoring, structural health monitoring
• Communications: Signal detection, modulation analysis, interference identification
• Biomedical: EEG/ECG analysis, ultrasound imaging
• Astronomy: Signal detection in radio telescope data