SDFT vs. QDFT

sdft_vs_qdft.py

# Basic SDFT vs. QDFT showcase based on figures from
# "Sliding with a constant Q" by Russell Bradford

import matplotlib.pyplot as plot
import matplotlib.ticker as ticker
import numpy as np

from sdft import SDFT
from qdft import QDFT

sr = 44100  # sample rate in hertz
n  = sr//2  # test signal length in samples

t = np.arange(n) / sr                                     # test signal timestamps in seconds
f = np.array([100, 110, 120, 1000, 10000, 11000, 12000])  # test signal frequencies in hertz
x = np.mean(np.sin(2 * np.pi * f[:, None] * t), axis=0)   # test signal samples of shape (n)

sdft = SDFT(500)             # sdft plan
qdft = QDFT(sr, (50, sr/2))  # qdft plan

ylin = sdft.sdft(x)  # total sdft matrix of shape (n, sdft.size)
ylog = qdft.qdft(x)  # total qdft matrix of shape (n, qdft.size)

ylin = np.abs(ylin)[-1]  # last sdft vector of shape (sdft.size)
ylog = np.abs(ylog)[-1]  # last qdft vector of shape (qdft.size)

xlin = [np.arange(sdft.size), np.linspace(0, sr / 2, sdft.size)]  # sdft bin numbers and frequencies
xlog = [np.arange(qdft.size), qdft.frequencies]                   # qdft bin numbers and frequencies

figure, axes = plot.subplots(2, 1)

axes[0].plot(ylin)
axes[0].set_title('SDFT')
axes[0].set_xlabel('Bin number / frequency')
axes[0].set_ylabel('Magnitude response')

axes[1].plot(ylog)
axes[1].set_title('QDFT')
axes[1].set_xlabel('Bin number / frequency')
axes[1].set_ylabel('Magnitude response')

axes[0].xaxis.set_major_formatter(ticker.FuncFormatter(
    lambda t, p: f'{int(t)}\n{int(np.interp(t, xlin[0], xlin[1]))} Hz'))
axes[1].xaxis.set_major_formatter(ticker.FuncFormatter(
    lambda t, p: f'{int(t)}\n{int(np.interp(t, xlog[0], xlog[1]))} Hz'))

plot.tight_layout()
plot.show()