Audio Measurements using JAAA. Fons Adriaensen. 2nd Linux Audio Developers Conference ZKM Karlsruhe 28 April - 2 May 2004
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1 JAAA Audio Measurements using JAAA Fons Adriaensen 2nd Linux Audio Developers Conference ZKM Karlsruhe 28 April - 2 May 2004 JAAA 1 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
2 JAAA - Overview What is it? FFT based spectrum analysis Measuring noise Internals Demo Things to do Questions? JAAA 2 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
3 What is it? A signal generator and spectrum analyser. Checking performance of audio HW en SW. JAAA is a technical, not a musical tool. Linear frequency scales Designed for accurate measurements Requires some technical knowledge JAAA 3 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
4 FFT based spectrum analysis FT : Fourier Transform. Transforms function of time f (t) (a signal) into a function of frequency F(ω) (a spectrum). Operates on continuous (not sampled) functions. Can be reversed : no information is lost in the transform. DFT : Discrete Fourier Transform. Same as FT, but operating on discrete (sampled) signals,and producing a discrete (sampled) spectrum. FFT : Fast Fourier Transform. Optimized version of the DFT. FFTW3 : A very nice open source FFT library, used in many Linux applications. JAAA 4 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
5 FFT based spectrum analysis An N-point FFT replaces N/2 bandpass filters. Frequency step F = F samp /N. F samp = 44.1 khz, 1024 point FFT filters at 0, 43, 86, Hz. Could it be so simple?... JAAA 5 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
6 FFT based spectrum analysis N samples N / 2 complex outputs N / 2 specturm points Audio FFT Power calc A simple analyser JAAA 6 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
7 FFT based spectrum analysis What s going wrong? Filter shape is the FT of the input window. JAAA 7 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
8 FFT based spectrum analysis Rectangular window JAAA 8 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
9 FFT based spectrum analysis Raised cosine window JAAA 9 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
10 FFT based spectrum analysis Raised cosine JAAA window JAAA 10 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
11 FFT based spectrum analysis N samples N samples N / 2 complex outputs N / 2 spectrum points Audio Window FFT Power calc Display Analyser with windowing Multiplication before FFT is equivalent to convolution after FFT. A short convolution can be done by an FIR fiter, so... JAAA 11 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
12 FFT based spectrum analysis N samples N complex outputs N spectrum points N / 2 complex outputs Audio FFT Polyphase FIR Power calc Display JAAA analyser Polyphase FIR replaces windowing, and interpolates the spectrum. Feedback path added for averaging power over time. JAAA 12 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
13 FFT based spectrum analysis Filter responses spaced /2 maximum error = 0.25 db. More accurate measurements are possible by interpolation. JAAA 13 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
14 Measuring noise How can we measure noise? Let s try... JAAA 14 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
15 Measuring noise How can we measure noise? Let s try... Apparent noise level depends on FFT length, or bandwidth. JAAA 15 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
16 Measuring noise How can we measure noise? Let s try... Apparent noise level depends on FFT length, or bandwidth. A spectrum analyser can be used to measure noise density, N 0. N 0 is noise power per 1 Hz of bandwidth. Total noise power = N 0 B. The unit of N 0 is 1 / Hz, or db / Hz. Noise level = -10 db, F sample = 44.1 khz B = khz = dbhz N 0 = db/hz Noise level = -10 db, F sample = 48.0 khz B = khz = dbhz N 0 = db/hz JAAA 16 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
17 Internals ALSA JACK Circular buffer Analyser Display mapper GUI Generator Events and commands Markers Audio thread X events Main thread JAAA program architecture JAAA 17 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
18 Internals Spectrum points Pixels More pixels than spectrum points, the easy case. Spectrum points Pixels More spectrum points than pixels. Correct signal level display requires peak value Correct noise level display requires average value JAAA displays two traces in this case. JAAA 18 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
19 Internals P F Peak markers are calculated using 2nd order interpolation. JAAA 19 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
20 Demo PCM in JAAA PCM out JACK AMS Demo signal routing. JAAA 20 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
21 Things to do Clean up the code Documentation More signal generators Integrated noise calculation Trace memories JACK transport JAAA 21 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
22 JAAA Audio Measurements using JAAA Question time! JAAA 22 2nd LAD Conference, Karlsruhe, 28 April 2 May 2004 All rights reserved c 2004 F.Adriaensen
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