DSP Filter Library

A comprehensive JavaScript library for digital signal processing filter design and analysis, supporting both IIR and FIR filters with interactive visualization.

Features

$3

- IIR Filters: Butterworth, Chebyshev I, Chebyshev II, Elliptic, Linkwitz-Riley, Bessel
- FIR Filters: Windowed-sinc design with multiple window functions

$3

- Lowpass
- Highpass
- Bandpass
- Bandstop

$3

- Frequency Response: Magnitude and phase plots
- Time Domain: Impulse response, group delay, and phase delay
- Poles & Zeros: Z-plane visualization with unit circle
- Coefficients: Second-order sections (IIR) or tap coefficients (FIR)

$3

- Basic Windows: Rectangular, Hann, Hamming, Blackman
- Advanced Blackman Variants: Blackman-Harris, Blackman-Nuttall, Nuttall, Exact Blackman
- Tapered Windows: Bartlett, Bartlett-Hann, Welch, Triangular, Tukey (with adjustable α)
- Specialized Windows: Gaussian (with adjustable σ), Poisson (with adjustable α), Parzen, Bohman, Lanczos, Cosine
- Advanced Windows: Flat-top, Dolph-Chebyshev, Taylor, Kaiser (with adjustable β)

Installation

bash

npm install dsp-filter-library





Usage



$3

javascript

import { FilterDSP } from 'dsp-filter-library';



// Design a 6th order Butterworth lowpass filter

const spec = {

  family: 'butter',

  kind: 'lowpass',

  N: 6,

  Fs: 48000,

  f1: 4000

};



const filter = FilterDSP.designIIR(spec);



// Get frequency response

const response = filter.frequencyGrid(1024);

console.log(response.magdB);    // Magnitude in dB

console.log(response.phaseDeg); // Phase in degrees

console.log(response.freqHz);   // Frequency points in Hz



// Get impulse response

const impResp = filter.impulseResponse(256);



// Get filter coefficients

console.log(filter.sections); // Second-order sections

$3

javascript

// Design a 101-tap Hamming window lowpass filter

const spec = {

  kind: 'lowpass',

  taps: 101,

  Fs: 48000,

  f1: 4000,

  window: 'hamming'

};



const filter = FilterDSP.designFIR(spec);



// Get filter taps

console.log(filter.taps);



// Get zeros

console.log(filter.zeros());

$3

javascript

// Kaiser window with custom β parameter

const kaiserFilter = FilterDSP.designFIR({

  kind: 'lowpass',

  taps: 101,

  Fs: 48000,

  f1: 4000,

  window: 'kaiser',

  beta: 8.6  // Adjustable sidelobe level

});



// Tukey window with custom α parameter

const tukeyFilter = FilterDSP.designFIR({

  kind: 'bandpass',

  taps: 201,

  Fs: 48000,

  f1: 2000,

  f2: 8000,

  window: 'tukey',

  alpha: 0.5  // Taper ratio (0=rectangular, 1=hann)

});



// Gaussian window with custom σ parameter

const gaussianFilter = FilterDSP.designFIR({

  kind: 'highpass',

  taps: 151,

  Fs: 48000,

  f1: 6000,

  window: 'gauss',

  sigma: 0.4  // Width parameter

});



// Flat-top window for accurate measurements

const flatTopFilter = FilterDSP.designFIR({

  kind: 'lowpass',

  taps: 301,

  Fs: 48000,

  f1: 4000,

  window: 'flatTop'  // Optimized for amplitude accuracy

});

$3

javascript

// Elliptic bandpass filter with custom ripple

const spec = {

  family: 'ellip',

  kind: 'bandpass',

  N: 8,

  Rp: 1.0,    // Passband ripple (dB)

  Rs: 60,     // Stopband ripple (dB)

  Fs: 48000,

  f1: 2000,   // Lower cutoff

  f2: 8000    // Upper cutoff

};



const filter = FilterDSP.designIIR(spec);





Interactive Demo



Open

example/index.html

 in your browser to see the interactive filter design tool with real-time visualization.



$3

- Real-time parameter adjustment with sliders and dropdowns

- Tabbed interface for different analysis views (Frequency, Time Domain, Poles & Zeros, Coefficients)

- Properly centered poles and zeros visualization with unit circle

- Fixed y-axis ranges for consistent comparison (Group Delay: -50 to +50 samples)

- 23 window functions with dynamic parameter controls

- Complete coefficient display (all FIR taps, all IIR sections)

- Responsive design with modern dark theme

- Real-time filter redesign on parameter changes



API Reference



$3



Designs an IIR filter based on the specification object.



Parameters:

-

spec.family

: Filter family ('butter', 'cheby1', 'cheby2', 'ellip', 'linkwitz', 'bessel')

-

spec.kind

: Filter type ('lowpass', 'highpass', 'bandpass', 'bandstop')

-

spec.N

: Filter order

-

spec.Rp

: Passband ripple in dB (for Chebyshev I and Elliptic)

-

spec.Rs

: Stopband ripple in dB (for Chebyshev II and Elliptic)

-

spec.Fs

: Sampling frequency in Hz

-

spec.f1

: First cutoff frequency in Hz

-

spec.f2

: Second cutoff frequency in Hz (for bandpass/bandstop)



$3



Designs an FIR filter using windowed-sinc method.



Parameters:

-

spec.kind

: Filter type ('lowpass', 'highpass', 'bandpass', 'bandstop')

-

spec.taps

: Number of filter taps (must be odd)

-

spec.Fs

: Sampling frequency in Hz

-

spec.f1

: First cutoff frequency in Hz

-

spec.f2

: Second cutoff frequency in Hz (for bandpass/bandstop)

-

spec.window

: Window function (see supported windows below)

-

spec.beta

: Kaiser window β parameter (default: 8.6)

-

spec.alpha

: Tukey window α parameter (default: 0.5)

-

spec.sigma

: Gaussian window σ parameter (default: 0.4)

-

spec.poissonAlpha

: Poisson window α parameter (default: 2.0)



Supported Window Functions:

-

'rect', 'hann', 'hamming', 'blackman'

'blackmanHarris', 'blackmanNuttall', 'nuttall', 'exactBlackman'

'bartlett', 'bartlettHann', 'welch', 'triangular'

'gauss', 'tukey', 'poisson', 'parzen', 'bohman'

'lanczos', 'cosine', 'flatTop', 'dolphChebyshev', 'taylor', 'kaiser'





$3



#### frequencyGrid(nPoints)

Returns frequency response data.

-

nPoints

: Number of frequency points to compute



Returns:

-

magdB

: Magnitude response in dB

-

phaseDeg

: Phase response in degrees (unwrapped)

-

freqHz

: Frequency points in Hz

-

gdSamples

: Group delay in samples

-

pdSamples

: Phase delay in samples



#### impulseResponse(nSamples)

Returns impulse response data.

-

nSamples

: Number of samples to compute



#### sections (IIR only)

Array of second-order sections with coefficients

a and b

.



#### taps (FIR only)

Array of filter tap coefficients.



#### zeros()

Returns array of filter zeros as complex numbers.



#### zPoles (IIR only)

Array of filter poles as complex numbers.



#### zZeros (IIR only)

Array of filter zeros as complex numbers.



Building

bash

npm install

npm run build





This will generate the library files in the

lib/

 directory:

-

dsp-filter-library.js

 - UMD build

-

dsp-filter-library.min.js

 - Minified UMD build

-

dsp-filter-library.esm.min.js

 - ES module build



Advanced Window Functions



The library includes 23 different window functions for FIR filter design, each with specific characteristics:



$3

- Rectangular: Sharpest transition, highest sidelobes

- Hann: Good balance of main lobe width and sidelobe level

- Hamming: Optimized for reduced first sidelobe

- Blackman: Lower sidelobes, wider main lobe



$3

- Blackman-Harris: 4-term window with very low sidelobes

- Blackman-Nuttall: Alternative 4-term window

- Nuttall: Another 4-term variant

- Exact Blackman: 3-term with exact coefficients



$3

- Bartlett: Triangular window

- Bartlett-Hann: Hybrid triangular-cosine window

- Welch: Parabolic window

- Tukey: Raised cosine with adjustable taper (α parameter)



$3

- Gaussian: Adjustable width (σ parameter)

- Poisson: Exponential decay (α parameter)

- Parzen: Smooth polynomial window

- Bohman: Smooth window with good sidelobe suppression

- Lanczos: Sinc-based window

- Cosine: Simple cosine window



$3

- Flat-top: Optimized for accurate amplitude measurements

- Dolph-Chebyshev: Controlled sidelobe level

- Taylor: Antenna design window

- Kaiser: Adjustable sidelobe level (β parameter)



Examples



$3

javascript

// Design a lowpass filter for audio

const filter = FilterDSP.designIIR({

  family: 'butter',

  kind: 'lowpass',

  N: 4,

  Fs: 44100,

  f1: 8000

});



// Process audio samples

const audioSamples = [/ your audio data /];

const filteredSamples = filter.process(audioSamples);

$3

javascript

// Analyze filter characteristics

const response = filter.frequencyGrid(2048);



// Find -3dB cutoff frequency

const cutoffIndex = response.magdB.findIndex(mag => mag <= -3);

const cutoffFreq = response.freqHz[cutoffIndex];



// Check stability (poles inside unit circle)

const isStable = filter.zPoles.every(pole => 

  Math.sqrt(pole.re  pole.re + pole.im  pole.im) < 1

);

License

MIT License - see LICENSE file for details.

Contributing

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests if applicable
5. Submit a pull request

Changelog

$3

- Expanded Window Functions: Added 23 different window functions (from 5 to 23)
- Advanced Window Parameters: Added adjustable parameters for Kaiser (β), Tukey (α), Gaussian (σ), and Poisson (α)
- Enhanced UI: Dynamic parameter controls that show/hide based on selected window
- Complete Coefficient Display: Show all FIR taps and IIR sections without truncation
- Fixed Poles and Zeros Visualization: Properly centered poles and zeros with unit circle
- Improved Group Delay Plot: Fixed y-axis range (-50 to +50 samples) for consistent comparison
- Enhanced Interactive Demo: Real-time parameter adjustment with comprehensive window selection
- Comprehensive Documentation: Updated README with all new features and window function details

$3

- Fixed poles and zeros visualization centering
- Improved group delay plot with fixed y-axis range
- Enhanced interactive demo interface
- Added comprehensive documentation

DSP Filter Library

A comprehensive JavaScript library for digital signal processing filter design and analysis, supporting both IIR and FIR filters with interactive visualization.

Features

$3

- IIR Filters: Butterworth, Chebyshev I, Chebyshev II, Elliptic, Linkwitz-Riley, Bessel
- FIR Filters: Windowed-sinc design with multiple window functions

$3

- Lowpass
- Highpass
- Bandpass
- Bandstop

$3

Installation

bash

npm install dsp-filter-library





Usage



$3

javascript

import { FilterDSP } from 'dsp-filter-library';



// Design a 6th order Butterworth lowpass filter

const spec = {

  family: 'butter',

  kind: 'lowpass',

  N: 6,

  Fs: 48000,

  f1: 4000

};



const filter = FilterDSP.designIIR(spec);



// Get frequency response

const response = filter.frequencyGrid(1024);

console.log(response.magdB);    // Magnitude in dB

console.log(response.phaseDeg); // Phase in degrees

console.log(response.freqHz);   // Frequency points in Hz



// Get impulse response

const impResp = filter.impulseResponse(256);



// Get filter coefficients

console.log(filter.sections); // Second-order sections

$3

javascript

// Design a 101-tap Hamming window lowpass filter

const spec = {

  kind: 'lowpass',

  taps: 101,

  Fs: 48000,

  f1: 4000,

  window: 'hamming'

};



const filter = FilterDSP.designFIR(spec);



// Get filter taps

console.log(filter.taps);



// Get zeros

console.log(filter.zeros());

$3

javascript

// Kaiser window with custom β parameter

const kaiserFilter = FilterDSP.designFIR({

  kind: 'lowpass',

  taps: 101,

  Fs: 48000,

  f1: 4000,

  window: 'kaiser',

  beta: 8.6  // Adjustable sidelobe level

});



// Tukey window with custom α parameter

const tukeyFilter = FilterDSP.designFIR({

  kind: 'bandpass',

  taps: 201,

  Fs: 48000,

  f1: 2000,

  f2: 8000,

  window: 'tukey',

  alpha: 0.5  // Taper ratio (0=rectangular, 1=hann)

});



// Gaussian window with custom σ parameter

const gaussianFilter = FilterDSP.designFIR({

  kind: 'highpass',

  taps: 151,

  Fs: 48000,

  f1: 6000,

  window: 'gauss',

  sigma: 0.4  // Width parameter

});



// Flat-top window for accurate measurements

const flatTopFilter = FilterDSP.designFIR({

  kind: 'lowpass',

  taps: 301,

  Fs: 48000,

  f1: 4000,

  window: 'flatTop'  // Optimized for amplitude accuracy

});

$3

javascript

// Elliptic bandpass filter with custom ripple

const spec = {

  family: 'ellip',

  kind: 'bandpass',

  N: 8,

  Rp: 1.0,    // Passband ripple (dB)

  Rs: 60,     // Stopband ripple (dB)

  Fs: 48000,

  f1: 2000,   // Lower cutoff

  f2: 8000    // Upper cutoff

};



const filter = FilterDSP.designIIR(spec);





Interactive Demo



Open

example/index.html

 in your browser to see the interactive filter design tool with real-time visualization.



$3

- Real-time parameter adjustment with sliders and dropdowns

- Tabbed interface for different analysis views (Frequency, Time Domain, Poles & Zeros, Coefficients)

- Properly centered poles and zeros visualization with unit circle

- Fixed y-axis ranges for consistent comparison (Group Delay: -50 to +50 samples)

- 23 window functions with dynamic parameter controls

- Complete coefficient display (all FIR taps, all IIR sections)

- Responsive design with modern dark theme

- Real-time filter redesign on parameter changes



API Reference



$3



Designs an IIR filter based on the specification object.



Parameters:

-

spec.family

: Filter family ('butter', 'cheby1', 'cheby2', 'ellip', 'linkwitz', 'bessel')

-

spec.kind

: Filter type ('lowpass', 'highpass', 'bandpass', 'bandstop')

-

spec.N

: Filter order

-

spec.Rp

: Passband ripple in dB (for Chebyshev I and Elliptic)

-

spec.Rs

: Stopband ripple in dB (for Chebyshev II and Elliptic)

-

spec.Fs

: Sampling frequency in Hz

-

spec.f1

: First cutoff frequency in Hz

-

spec.f2

: Second cutoff frequency in Hz (for bandpass/bandstop)



$3



Designs an FIR filter using windowed-sinc method.



Parameters:

-

spec.kind

: Filter type ('lowpass', 'highpass', 'bandpass', 'bandstop')

-

spec.taps

: Number of filter taps (must be odd)

-

spec.Fs

: Sampling frequency in Hz

-

spec.f1

: First cutoff frequency in Hz

-

spec.f2

: Second cutoff frequency in Hz (for bandpass/bandstop)

-

spec.window

: Window function (see supported windows below)

-

spec.beta

: Kaiser window β parameter (default: 8.6)

-

spec.alpha

: Tukey window α parameter (default: 0.5)

-

spec.sigma

: Gaussian window σ parameter (default: 0.4)

-

spec.poissonAlpha

: Poisson window α parameter (default: 2.0)



Supported Window Functions:

-

'rect', 'hann', 'hamming', 'blackman'

'blackmanHarris', 'blackmanNuttall', 'nuttall', 'exactBlackman'

'bartlett', 'bartlettHann', 'welch', 'triangular'

'gauss', 'tukey', 'poisson', 'parzen', 'bohman'

'lanczos', 'cosine', 'flatTop', 'dolphChebyshev', 'taylor', 'kaiser'





$3



#### frequencyGrid(nPoints)

Returns frequency response data.

-

nPoints

: Number of frequency points to compute



Returns:

-

magdB

: Magnitude response in dB

-

phaseDeg

: Phase response in degrees (unwrapped)

-

freqHz

: Frequency points in Hz

-

gdSamples

: Group delay in samples

-

pdSamples

: Phase delay in samples



#### impulseResponse(nSamples)

Returns impulse response data.

-

nSamples

: Number of samples to compute



#### sections (IIR only)

Array of second-order sections with coefficients

a and b

.



#### taps (FIR only)

Array of filter tap coefficients.



#### zeros()

Returns array of filter zeros as complex numbers.



#### zPoles (IIR only)

Array of filter poles as complex numbers.



#### zZeros (IIR only)

Array of filter zeros as complex numbers.



Building

bash

npm install

npm run build





This will generate the library files in the

lib/

 directory:

-

dsp-filter-library.js

 - UMD build

-

dsp-filter-library.min.js

 - Minified UMD build

-

dsp-filter-library.esm.min.js

 - ES module build



Advanced Window Functions



The library includes 23 different window functions for FIR filter design, each with specific characteristics:



$3

- Rectangular: Sharpest transition, highest sidelobes

- Hann: Good balance of main lobe width and sidelobe level

- Hamming: Optimized for reduced first sidelobe

- Blackman: Lower sidelobes, wider main lobe



$3

- Blackman-Harris: 4-term window with very low sidelobes

- Blackman-Nuttall: Alternative 4-term window

- Nuttall: Another 4-term variant

- Exact Blackman: 3-term with exact coefficients



$3

- Bartlett: Triangular window

- Bartlett-Hann: Hybrid triangular-cosine window

- Welch: Parabolic window

- Tukey: Raised cosine with adjustable taper (α parameter)



$3

- Gaussian: Adjustable width (σ parameter)

- Poisson: Exponential decay (α parameter)

- Parzen: Smooth polynomial window

- Bohman: Smooth window with good sidelobe suppression

- Lanczos: Sinc-based window

- Cosine: Simple cosine window



$3

- Flat-top: Optimized for accurate amplitude measurements

- Dolph-Chebyshev: Controlled sidelobe level

- Taylor: Antenna design window

- Kaiser: Adjustable sidelobe level (β parameter)



Examples



$3

javascript

// Design a lowpass filter for audio

const filter = FilterDSP.designIIR({

  family: 'butter',

  kind: 'lowpass',

  N: 4,

  Fs: 44100,

  f1: 8000

});



// Process audio samples

const audioSamples = [/ your audio data /];

const filteredSamples = filter.process(audioSamples);

$3

javascript

// Analyze filter characteristics

const response = filter.frequencyGrid(2048);



// Find -3dB cutoff frequency

const cutoffIndex = response.magdB.findIndex(mag => mag <= -3);

const cutoffFreq = response.freqHz[cutoffIndex];



// Check stability (poles inside unit circle)

const isStable = filter.zPoles.every(pole => 

  Math.sqrt(pole.re  pole.re + pole.im  pole.im) < 1

);

License

MIT License - see LICENSE file for details.

Contributing

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests if applicable
5. Submit a pull request

Changelog

$3

- Fixed poles and zeros visualization centering
- Improved group delay plot with fixed y-axis range
- Enhanced interactive demo interface
- Added comprehensive documentation