New Version VecLab 2.0 of Swift Real/Complex Vector DSP Library

Related Projects Swift Numerics
, , ,
1

Hello! I’ve updated my VecLab DSP package to follow more Swift-like conventions. The package uses Accelerate to provide real and complex vector operations. Here’s a quick summary of its features:

  • Mixed scalar, vector, real and complex operators: +, -, *, \
  • Power operator **
  • Vectorized operations and functions using Accelerate
  • DSP functions like fft, ifft, ifftshift

Originally, VecLab was designed to quickly to port MATLAB code into Swift. It used tuples to represent complex numbers and arrays . Good enough for porting, but it became awkward for writing new Swift-native code. As the package developed into a more standalone DSP toolkit, I decided it was time to update the design.

VecLab 2.0

The biggest change is to complex scalars and arrays. Complex arrays are stored as split complex real and imaginary arrays for compatibility with VDSP, but now conform to the Collection protocol.

  • ComplexDouble struct conforms to SignedNumeric protocol.
  • ComplexDoubleArray struct conforms to Collection protocol.
  • Get and set Index ranges: a[2...4] = b[10...12]
  • Ranges can have an optional step parameter : a[2...4, 2] = b[10...12, 2]

GitHub

Documentation

You can find the DocC documention hosted on the Swift Package Index site:

VecLab Online Documentation
VecLab SwiftPackage Index Page

Example: Chirp Z-Transform (CZT)

Here’s an example of computing the Chirp Z-Transform using VecLab. The CZT allows you to perform FFT-like transforms of arbitrary length (non-power-of-2), useful for spectral zooming and frequency analysis with higher resolution in selected regions.

This implementation is based on the Chirp Z-Transform Spectral Zoom Optimization with MATLAB document.

func czt(_ x: ComplexArray, k: Int? = nil, w: Complex? = nil, a: Complex? = nil) -> ComplexArray {

    // Handle input parameters
    let m = x.count
    let k = k ?? m
    let w = w ?? expi(-2.0 * .pi / Double(k)) // expi is shortcut for Euler cos(x) + sin(x)*i
    let a = a ?? Complex(1.0, 0.0)
    
    // Length for power-of-two FFT
    let nfft = Int(2 ** nextpow2(m+k-1))
    
    // Premultiply data
    let kk = vector((-m+1) ... max(k-1, m-1))
    let kk2 = (kk ** 2.0) / 2.0
    let ww = w ** kk2  // Chirp filter is 1./ww
    
    // Apply initial twiddle factor
    let nn = vector(0 ... (m-1))
    var aa = a ** nn
    
    aa = aa * ww[m-1 ..< m+m-1]
    let y = x * aa
    
    let inv_ww = 1.0 / ww[0 ..< (m+k-1)] //  <----- Chirp filter.

    // Fast convolution via FFT zero padded to length
    var fy = fft(y, length: nfft)
    let fv = fft(inv_ww, length: nfft)
    fy = fy * fv
    var g = ifft(fy)
    
    // Final multiply
    g = g[m-1 ..< (m+k-1)] * ww[m-1 ..< (m+k-1)]
        
    return g
}

Expanded Functions

VecLab now includes a wide range of functions inspired by MATLAB and NumPy. Most operations support real or complex inputs, with scalar or vector types.

Group Functions
Arrays arange, cat, circshift, dot, flip, length, ones, paddata, repelem, resize, slice, trimdata, zeros
Basic abs, cumprod, cumsum, disp, iterate, norm, prod, sign, sum
Complex abs, angle, conj, cplxpair, imag, real, unwrap, wrapTo2Pi, wrapToPi
Conversion cart2pol, cart2sph, d2f, db2mag, db2pow, deg2rad, f2d, mag2db, pol2cart, pow2db, rad2deg, sph2cart
Discrete factor, factorial, gcd, isprime, lcm, nextprime, nchoosek, perms, prevprime, primes
Exponents exp, expi, log, log2, log10, nextpow2, sqrt
FFT dft, dftr, fft, fftr, fftshift, fftsymmetric, idft, idftr, ifft, ifftr, ifftshift
Filter biquad, freqz, filter
Integration diff, gradient, trapz
Interpolation interp1, interpft, sincresample
Modulo ceil, fix, floor, mod, rem, round, trunc
Optimization fminbnd, fminsearch
Power pow
Random awgn, rand, randn, rng
Smoothing hampel, medfilt1
Space freqspace, linspace, logspace
Special besseli0, sinc
Statistics histcounts, max, maxindex, mean, median, min, minindex, mode, rms, stddev, variance
Timing tic, toc, timeit
Trigonometry acos, asin, atan, atan2, cos, sin, tan
Window blackman, blackmanharris, flattopwin, gausswin, hamming, hann, kaiser, tukeywin, rectwin
5 Likes