Filter Design Tool

Design and analyze low-pass, high-pass, and band-pass filters

Filter Configuration

Display Options

Frequency Response

Magnitude Response

Phase Response

Filter Characteristics

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Filter Types
  • Low-Pass: Allows frequencies below the cutoff frequency to pass through while attenuating higher frequencies. Common uses: audio smoothing, anti-aliasing, noise reduction.
  • High-Pass: Allows frequencies above the cutoff frequency to pass through while attenuating lower frequencies. Common uses: removing DC offset, bass reduction, AC coupling.
  • Band-Pass: Allows frequencies within a specific range (between lower and upper cutoff) to pass through. Common uses: channel selection, tone detection, signal isolation.
Filter Designs
  • Butterworth: Provides maximally flat response in the passband with no ripple. Smooth rolloff characteristics. Best for applications requiring flat frequency response.
  • Chebyshev: Provides steeper rolloff than Butterworth but with ripple in the passband. Better selectivity at the cost of passband flatness.
Understanding Filter Order

Filter order determines the steepness of the rolloff:

  • 1st Order: 6 dB/octave (20 dB/decade) rolloff - gentle transition
  • 2nd Order: 12 dB/octave (40 dB/decade) rolloff - moderate transition
  • 3rd Order: 18 dB/octave (60 dB/decade) rolloff - sharp transition
  • 4th Order: 24 dB/octave (80 dB/decade) rolloff - very sharp transition

Higher order filters provide better frequency selectivity but may introduce more phase distortion and require more complex implementation.

Key Concepts
  • Cutoff Frequency (-3dB point): The frequency at which the signal is attenuated by 3 dB (approximately 0.707 or 70.7% of the passband amplitude).
  • Magnitude Response: Shows how the filter amplifies or attenuates different frequencies. Measured in dB (decibels).
  • Phase Response: Shows the phase shift introduced by the filter at different frequencies. Important for applications requiring phase coherence.
  • Group Delay: The derivative of phase with respect to frequency. Represents the time delay for different frequency components.
  • Rolloff Rate: How quickly the filter attenuates signals outside the passband, measured in dB/octave or dB/decade.
Practical Applications
  • Audio Processing: Equalizers, crossover networks for speakers, noise reduction
  • Communications: Channel filtering, interference rejection, modulation/demodulation
  • Instrumentation: Anti-aliasing before ADC, smoothing sensor data, EMI/RFI filtering
  • Signal Analysis: Isolating frequency components, spectral analysis, feature extraction