Towards High Quality Real-Time Signal Reconstruction from STFT Magnitude

Zdeněk Průša
Abstract:

An efficient algorithm for real-time signal reconstruction from the magnitude of the Short-time Fourier transform (STFT) is presented. The algorithm combines advantages of two previously published algorithms and the reconstructed signals exhibit very good perceptual quality.

We present an extensive comparison with the state-of-the-art algorithms which shows that the proposed method outperforms others by far in settings capable of producing high quality signals.

The preprint is available here ltfatnote048.pdf. Note that it might differ from the published version.

Additional content:

The following table show errors in dB for all 70 samples from the EBU SQAM database for the proposed algorithm (RTPGHI(1) + GSRTISI-LA(1)) and for RTPGHI(1), RTISI-LA(2), GSRTISI-LA(2) and SPSI + GSRTISI-LA(2). The number in the brackets denotes the number of look-ahead frames used. The number of per-frame iterations was fixed to 24.

The playback can be started by selecting one of the table cells. All the files were compressed by oggenc from vorbis-tools 1.4.0 with the default settings. Your browser must support HTML5 audio player and it must be able to decode ogg files. Alternativelly an archive containing all the files compressed using lossless flac encoder can be downloaded from here.

Table 1: Addendum to Fig. 1. and Fig. 2.

Loaded file: None
Truncated Gaussian window
Original 
RTPGHI(1)
 
RTISI-LA(2)
 
GSRTISI-LA(2)
 
SPSI+
GSRTISI-LA(2)

RTPGHI(1)+
GSRTISI-LA(1)
(proposed)
01 Sine wave, 1 kHz −53.19 −49.32 −54.10 −51.55 −59.70
02 Pink noise −18.46 −17.92 −25.38 −21.46 −32.83
03 Electronic gong −51.21 −39.36 −52.58 −50.92 −52.43
04 Electronic gong −52.41 −39.43 −55.87 −51.96 −58.19
05 Electronic gong −58.16 −39.58 −65.46 −59.18 −67.43
06 Electronic gong −40.66 −34.46 −41.35 −42.59 −60.05
07 Electronic tune −43.34 −37.74 −61.00 −52.29 −60.98
08 Violin −26.45 −31.70 −38.47 −39.01 −45.30
09 Viola −27.64 −32.65 −39.06 −38.53 −46.86
10 Violoncello −29.58 −33.39 −42.50 −39.69 −48.55
11 Double-bass −29.41 −33.49 −42.15 −37.22 −42.47
12 Picollo −33.61 −35.39 −41.28 −40.60 −49.74
13 Flute −31.85 −35.22 −42.46 −42.53 −50.96
14 Oboe −31.50 −30.95 −37.35 −36.57 −47.65
15 Cor anglais −29.22 −32.76 −39.29 −40.69 −47.78
16 Clarinet −31.52 −38.17 −44.63 −46.17 −47.25
17 Bass-clarinet −31.95 −39.55 −44.79 −44.50 −48.63
18 Bassoon −27.53 −29.74 −34.04 −33.86 −45.94
19 Contra-bassoon −20.40 −20.38 −25.12 −23.06 −29.21
20 Saxophone −31.68 −33.22 −37.53 −40.30 −48.03
21 Trumpet −35.07 −33.84 −41.23 −39.27 −45.64
22 Trombone −33.99 −36.87 −42.83 −40.84 −47.76
23 Horn −28.99 −29.78 −35.96 −33.61 −42.46
24 Tuba −31.64 −34.50 −44.30 −41.55 −47.45
25 Harp −24.68 −25.40 −31.94 −28.81 −33.91
26 Claves −25.97 −17.08 −19.92 −21.71 −40.52
27 Castanets −22.22 −13.24 −15.12 −17.05 −30.73
28 Side drum −29.79 −22.01 −26.44 −25.49 −49.09
29 Bass drum −23.54 −20.29 −24.74 −22.65 −33.58
30 Kettle-drums −23.18 −20.54 −23.28 −24.74 −33.79
31 Cymbal −21.75 −20.49 −23.74 −24.21 −36.62
32 Triangle −39.62 −31.07 −34.85 −37.87 −50.87
33 Gong −20.06 −19.67 −24.61 −23.00 −35.07
34 Tubular bells −26.62 −29.20 −34.68 −32.46 −43.03
35 Glockenspiel −37.64 −28.55 −31.18 −33.69 −52.66
36 Xylophone −27.31 −21.11 −23.90 −28.07 −39.45
37 Vibraphone −23.99 −26.02 −31.44 −37.06 −44.34
38 Marimba −34.44 −32.95 −36.21 −37.94 −48.45
39 Grand piano −28.02 −26.87 −31.49 −30.80 −37.82
40 Harpsichord −23.95 −24.69 −27.43 −28.21 −38.80
41 Celesta −31.77 −29.27 −37.03 −34.75 −43.25
42 Accordion −25.27 −29.02 −37.32 −34.67 −42.29
43 Organ −32.47 −33.98 −40.53 −40.09 −44.60
44 Soprano −29.77 −29.12 −37.93 −36.37 −46.65
45 Alto −26.47 −26.80 −34.91 −32.26 −39.64
46 Tenor −27.41 −27.78 −35.18 −31.92 −41.86
47 Bass −23.30 −24.07 −29.82 −27.58 −38.48
48 Quartet −23.51 −24.29 −31.57 −29.21 −38.72
49 Female speech eng. −27.33 −22.84 −26.42 −26.27 −34.52
50 male speech eng. −29.39 −24.04 −27.62 −27.67 −37.15
51 Female speech fra. −30.94 −26.42 −31.26 −31.34 −39.79
52 male speech fra. −27.20 −22.96 −26.44 −25.54 −31.65
53 Female speech ger. −23.62 −23.78 −26.78 −26.74 −29.14
54 Male speech ger. −28.98 −24.15 −27.76 −27.43 −35.41
55 Trumpet-Haydn −25.74 −24.81 −29.97 −29.30 −37.60
56 Organ-Handel −21.47 −23.71 −29.98 −27.58 −36.74
57 Organ-Bach −21.12 −21.84 −26.69 −23.70 −28.72
58 Guitar-Sarasate −26.12 −24.48 −28.50 −29.20 −37.45
59 Violin-Ravel −23.59 −28.37 −36.45 −34.74 −42.07
60 Piano-Schubert −24.13 −23.90 −29.66 −29.64 −38.61
61 Soprano-Mozart −24.27 −23.23 −29.86 −27.12 −38.75
62 Soprano-Spiritual −26.47 −26.80 −32.76 −32.02 −41.64
63 Soloists-Verdi −22.99 −19.80 −25.16 −23.42 −35.54
64 Choir-Orff −21.29 −21.72 −28.52 −25.50 −34.44
65 Orchestra-Strauss −14.91 −21.07 −35.16 −36.90 −38.18
66 Wind ensemble-Stravinsky −21.12 −21.27 −28.21 −25.59 −31.93
67 Wind ensemble-Mozart −28.22 −27.85 −37.37 −34.30 −43.98
68 Orchestra-Baird −20.58 −20.64 −25.31 −24.44 −35.75
69 ABBA −25.56 −21.31 −24.93 −25.31 −33.81
70 Eddie Rabbitt −23.61 −22.38 −26.63 −25.95 −34.47