THD+N calculator

readme.txt

Somewhat crude THD+N calculator in Python

Measures the total harmonic distortion plus noise (THD+N) for a given input 
signal, by guessing the fundamental frequency (finding the peak in the FFT), 
and notching it out in the frequency domain.

Depends on Audiolab and SciPy
* http://www.ar.media.kyoto-u.ac.jp/members/david/softwares/audiolab/
* http://www.scipy.org/

Example of usage, with 997 Hz full-scale sine wave generated by Adobe Audition 
at 96 kHz, showing the 16-bit quantization distortion:

> python thdcalculator.py "perfect 997 Hz no dither.flac"
Frequency:	997.000000 Hz
THD+N:  	0.0016% or -96.1 dB

(Is this right?  Theoretical SNR of a FS sine is 1.761+6.02*16 = -98.09 dB.  
Close, at least.)

According to the never-wrong Wikipedia:
* THD is the fundamental alone vs the harmonics alone
* THD+N is the entire signal (not just the fundamental) vs the entire signal 
with the fundamental notched out.  (For low distortion, the difference between 
the entire signal and the fundamental is negligible.)

The primary problem with the current script is that I don't know how much of 
the surrounding region of the peak to throw away.  Probably the way to match 
other test equipment is to just calculate the width of a certain bandwidth, 
but is that really ideal?

width = 50
f[i-width: i+width+1] = 0

Instead of a fixed width, it currently just tries to find the nearest local 
minima and throw away everything between them.  It works for almost all cases, 
but on peaks with wider "skirts", it gets stuck at any notches.  Should this 
be considered part of the peak or part of the noise (jitter)?

By comparison, Audio Precision manual states "Bandreject Response typically 
–3 dB at 0.725 f0 & 1.38 f0", which is about 0.93 octaves.

Also it computes the FFT for the entire sample, which is a waste of time.  Use 
short samples.

Adobe Audition with dither:
997 Hz 8-bit    -49.8
997 Hz 16-bit   -93.4
997 Hz 32-bit   -143.9

Art Ludwig's Sound Files (http://members.cox.net/artludwig/):
File                Claimed  Measured  (dB)
Reference           0.0%     0.0022%   -93.3
Single-ended triode 5.0%     5.06%     -25.9
Solid state         0.5%     0.51%     -45.8

Comparing a test device on an Audio Precision System One 22 kHz filtered vs 
recorded into my 96 kHz 24-bit sound card and measured with this script:

Frequency   AP THD+N    Script THD+N
40          1.00%       1.04%
100         0.15%       0.19%
100         0.15%       0.14%
140         0.15%       0.17%
440         0.056%      0.057%
961         0.062%      0.067%
1021        0.080%      0.082%
1440        0.042%      0.041%
1483        0.15%       0.15%
4440        0.048%      0.046%
9974        7.1%        7.8%
10036       0.051%      0.068%
10723       8.2%        9.3%
13640       12.2%       16.8%
19998       20.2%       56.3%  (nasty intermodulation distortion)
20044       0.22%       0.30%

So it's mostly accurate.   Mostly.

thdncalculator.py

from __future__ import division
import sys
from scikits.audiolab import Sndfile
from scipy.signal import blackmanharris
from numpy.fft import rfft, irfft
from numpy import argmax, sqrt, mean, absolute, arange, log10
import numpy as np

def rms_flat(a):
    """Return the root mean square of all the elements of *a*, flattened out.
    
    """
    return sqrt(mean(absolute(a)**2))

def find_range(f, x):
    """Find range between nearest local minima from peak at index x
    
    """
    for i in arange(x+1, len(f)):
        if f[i+1] >= f[i]:
            uppermin = i
            break
    for i in arange(x-1, 0, -1):
        if f[i] <= f[i-1]:
            lowermin = i + 1
            break
    return (lowermin, uppermin)

def THDN(signal, sample_rate):
    # Get rid of DC and window the signal
    signal -= mean(signal) # TODO: Do this in the frequency domain, and take any skirts with it
    windowed = signal * blackmanharris(len(signal))  # TODO Kaiser?

    # Measure the total signal before filtering but after windowing
    total_rms = rms_flat(windowed)

    # Find the peak of the frequency spectrum (fundamental frequency), and filter 
    # the signal by throwing away values between the nearest local minima
    f = rfft(windowed)
    i = argmax(abs(f))
    print 'Frequency: %f Hz' % (sample_rate * (i / len(windowed))) # Not exact
    lowermin, uppermin = find_range(abs(f), i)
    f[lowermin: uppermin] = 0

    # Transform noise back into the signal domain and measure it
    # TODO: Could probably calculate the RMS directly in the frequency domain instead
    noise = irfft(f)
    THDN = rms_flat(noise) / total_rms
    print "THD+N:     %.4f%% or %.1f dB" % (THDN * 100, 20 * log10(THDN))

def load(filename):
    wave_file = Sndfile(filename, 'r')
    signal = wave_file.read_frames(wave_file.nframes)
    channels = wave_file.channels
    sample_rate = wave_file.samplerate
    return signal, sample_rate, channels
    
def analyze_file(filename):
    signal, sample_rate, channels = load(filename)

    print 'Analyzing "' + filename + '"...'

    if channels == 1:
        # Monaural
        THDN(signal, sample_rate)
    elif channels == 2:
        # Stereo
        if np.array_equal(signal[:,0],signal[:,1]):
            print '-- Left and Right channels are identical --'
            THDN(signal[:,0], sample_rate)
        else:
            print '-- Left channel --'
            THDN(signal[:,0], sample_rate)
            print '-- Right channel --'
            THDN(signal[:,1], sample_rate)
    else:
        # Multi-channel
        for ch_no, channel in enumerate(signal.transpose()):
            print '-- Channel %d --' % (ch_no + 1)
            THDN(channel, sample_rate)
    
    print '\n'

files = sys.argv[1:]
if files:
    for filename in files:
        #try:
        analyze_file(filename)
        #print 'No URL found in file', filename
else:
    sys.exit("You must provide at least one file to analyze")

Thanks for writing this. I find for simple waveforms, a flattop window is much more accurate. So I:

changed line 3 to: from scipy.signal import flattop
changed line 52 to: windowed = signal * flattop(len(signal)) #

That drastically increased my accuracy, but flattops have wider band effects so if you have a lot of different frequency content, this may not be the best window. A hanning window is another good option for audio data. Just my 2 cents. Thanks!

@tmbouman Yeah the newer version uses flattop HFT248D: https://github.com/endolith/waveform_analysis/blob/master/waveform_analysis/thd.py#L63

This is elaborate, thanks!
I am looking to do something similar but in a WinPE environment on a windows on arm device. Numpy and Scipy aren't available on windows on ARM64 yet. Is there a way to do this differently without them as dependency?

@ 200502002 I don't know about that platform, but you could re-implement this in another language.

I'm a newer in audio analyze and I'm trying to understand your code
In the line 51: Can you explain for me why need to do "signal -= mean(signal)", or did you have any document about your method?
Many thanks!

@KiDo-Ruan That's removing the DC offset, or bias, from the signal

I had use your code to calculated THD of some sample file and use APx500 machine calculated it and the result is the same (the AP use blackmanharris window too, probably :D). From your code, i want to develop it, if i want to plot the signal in frequency domain, Did you know how can i calculate amplitude of signal?
I had find out some example at stackoverflow but i don't know if they're doing it right.

@KiDo-Ruan What kind of plot are you trying to do? I have a stem plot for spectrum here https://gist.github.com/endolith/236567

FFT transforms signals from the time domain to the frequency domain, right?
I'm trying to plot time domain and frequency domain so that user can see the waveform before and after performing the FFT.
Thanks for your example, i had find out some example but most of them take fixed values ​​such as f, N. My problem is, how can i make it with a random wav file? like as analyze a 20Hz to 20kHz wav file.

@KiDo-Ruan

"see the waveform before and after performing the FFT"

Do you mean plot the waveform and the spectrum?

Have you seen https://gist.github.com/endolith/98acf9824dbf10a01795?

Have you tried asking ChatGPT to explain it and help you with the code?

It work for me. Thanks you!

I'm in Viet Nam, ChatGPT is not enabled in my country :|