Examples of digital signal processing in pure JavaScript. The code is adapted from node-fft (fft-js) and remains intended primarily for example purposes as it is not optimised for efficiency.
The lib/dsp.js file is nonetheless coded with reusability and portability in mind, such that it should be straightforward for developers to use part or all of the library of functions in either Node.js (ex: advlib-ble-gatt) or in client-side applications.
Examples are provided in the /bin folder, each of which can be run with the command npm run exampleName. Clone this repository and run the commands from its root folder.
Perform a Fast Fourier Transform on a time series of audio samples.
npm run fft
The example uses a 440Hz sine wave of amplitude 1 sampled at 44.1kHz using 32768 samples and should output the following:
Completed in ### ms
Peak magnitude of 0.9934 at 440.1HzEdit the parameters in bin/fft to test different scenarios.
Determine the velocity overall from a time series of acceleration samples.
npm run velocityoverall
The velocity overall is calculated as follows:
- Remove any DC offset from the samples
- Split into (up to 4) non-overlapping time series of at least 256 samples
- Application of Hann window to each time series using
hannWindow(samples) - Conversion to frequency domain using
fft(samples, samplingRate) - Integration over each frequency bin from 10Hz to 1000Hz to obtain velocities
- RMS of velocities divided by square root of Hann noise bandwidth
- Average of the (up to 4) overall velocities
Assuming acceleration samples are in m/s^2 and the samplingRate is in Hz, the velocity overall will be in m/s. The example uses a 63Hz sine wave of magnitude 1g (9.8m/s^2) sampled at 2560Hz using 4096 samples and should output the following:
Peak acceleration at 62.5Hz with 4.77m/s2 and 0.0121m/s
velocityOverall(Set 0): 0.01756m/s
Peak acceleration at 62.5Hz with 4.77m/s2 and 0.0121m/s
velocityOverall(Set 1): 0.01758m/s
Peak acceleration at 62.5Hz with 4.77m/s2 and 0.0121m/s
velocityOverall(Set 2): 0.01755m/s
Peak acceleration at 62.5Hz with 4.77m/s2 and 0.0121m/s
velocityOverall(Set 3): 0.01758m/s
velocityOverall(*Avg*): 0.01757m/s
Completed in ## msEdit the parameters in bin/velocityoverall to test different scenarios.
The lib/dsp.js file provides a JavaScript implementation of a Fast Fourier Transform (FFT), Hann window, and root mean square calculation.
Compute the Fast Fourier Transform of the given Array of samples captured at the given samplingRate (typically in Hz). For example, the original test case would be implemented as follows:
const dsp = require('./lib/dsp.js'); // Edit path as required
let samples = [ 1, 1, 1, 1, 0, 0, 0, 0 ];
let samplingRate = 44100;
console.log(dsp.fft(samples, samplingRate));
// {
// magnitudes: [ 4, 2.613125929752753, 0, 1.0823922002923938 ],
// frequencies: [ 0, 5512.5, 11025, 16537.5 ],
// numberOfBins: 4
// }Compute the Hann window of the given samples, returning the windowed samples as a new Array.
const dsp = require('./lib/dsp.js'); // Edit path as required
let values = [ 1, -1, 1, -1, 1 ];
console.log(dsp.hannWindow(values));
// [ 0, -0.4999999999999999, 1, -0.5000000000000001, 0 ]Compute the root mean square of the given Array of values, for example:
const dsp = require('./lib/dsp.js'); // Edit path as required
let values = [ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ];
console.log('The calculated RMS is', dsp.rms(values));
// The calculated RMS is 13.674794331177344Offset the given values by the given offset. If no offset is provided, the mean of the values will be used as the offset, effectively removing any DC offset from the values.
The values can be either an Array of Numbers of an Array of Array. In the latter case, the function will use self-recursion.
const dsp = require('./lib/dsp.js'); // Edit path as required
let values = [ 1, -1, 1, -1, 1 ];
console.log(dsp.dcOffset(values, 1));
// [ 2, 0, 2, 0, 2 ]
values = [ [ 1, 2 ], [ 3, 4 ], [ 5, 6 ] ];
console.log(dsp.dcOffset(values));
// [ [ -0.5, 0.5 ], [ -0.5, 0.5 ], [ -0.5, 0.5 ] ]Split the given samples into a set of subsamples, up to the given maximum number of subsamples, each of the given minimum length or a larger power of two, whichever is greater, for example:
const dsp = require('./lib/dsp.js'); // Edit path as required
let samples = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];
console.log(dsp.createPowerOfTwoLengthSubSamples(samples, 2, 2));
// [ [ 0, 1, 2, 3 ], [ 6, 7, 8, 9 ] ]
console.log(dsp.createPowerOfTwoLengthSubSamples(samples, 2, 4));
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