Welcome to fdls’s documentation!

This package implements the Frequency Domain Least Squares filter desing method.

Example

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import freqz

from fdls import fdls_design

NUMTAPS = 4096
SAMPLERATE = 44100

# create a desired magnitude spectrum
freq = np.linspace(0, SAMPLERATE/2, NUMTAPS)
phi = np.cumsum(np.logspace(2, 0, NUMTAPS))*2*np.pi/SAMPLERATE
magnitude = 0.5*np.cos(phi) - freq/SAMPLERATE + 1

# FDLS filter design of desired magnitude spectrum 
# with minimum phase calculated from magnitude spectrum
bcoef, acoef = fdls_design(
    ma_order=12, 
    ar_order=12, 
    magnitude=magnitude, 
    phase=None)

plt.semilogx(freq, 20*np.log10(magnitude))
freqz(
    bcoef, 
    acoef, 
    NUMTAPS, 
    fs=SAMPLERATE, 
    plot=lambda w,h: plt.semilogx(w, 20*np.log10(np.abs(h)), '--'))

plt.legend(['desired', 'fdls design'])
plt.grid(True)
plt.xlabel('Frequency in Hz')
plt.ylabel('Magnitude in dB(FS)')
plt.show()

(Source code, png, hires.png, pdf)

Implementation of the Frequency Domain Least Squares Filter Design Method according to Soderstrand and Berchin.

fdls.magnitude_to_minimumphase(magnitude, twosided=False)[source]

Returns minimumphase for given onesided magnitude spectrum.

Parameters:

magnitude (ArrayLike) – Magnitude spectrum (expects onesided magnitude spectrum by default)
twosided (bool) – Set to True if your given magnitude spectrum is twosided. Default: False

Returns:

Minimum phase (onesided) for given magnitude.

Return type:

phase (ndarray)

fdls.fdls_design(ma_order, ar_order, magnitude, phase, weights=None)[source]

Returns b,a filter coefficients (ARMA model) using Frequency Domain Least Squares method

Parameters:

ma_order (int) – Order of b coefficients i.e. numerator. Moving average part of the model.
ar_order (int) – Order of a coefficients i.e. denominator. Autregressive part of the model.
magnitude (ArrayLike[N]) – Magnitude of desired frequency response.
phase (None or ArrayLike[N]) – Phase of desired frequency response. If None, a minimum phase is calculated from the provided magnitude.
weights (None or ArrayLike[N]) – Frequency weighting or LS error.

Returns:

b, a Coefficients of numerator (optimal in least squares sense).

Return type:

b_coeffs, a_coeffs (Tuple[ndarray, ndarray])

Raises:

ValueError – If magnitude or phase are not real valued or not of the same length.
ValueError – If magnitude, phase (if given) and weights (if given) are not of the same length.

References

G. Berchin, “Precise Filter Design [DSP Tips & Tricks],” in IEEE Signal Processing Magazine, vol. 24, no. 1, pp. 137-139, Jan. 2007, DOI: 10.1109/MSP.2007.273077.

Michael A. Soderstrand, Gregory Berchin & Randy S. Roberts (1995) Frequency domain least-squares system identification, international journal of electronics, 78:1, 25-35, DOI: 10.1080/00207219508926137

Welcome to fdls’s documentation!

Example

Indices and tables