1. MP3 Audio Decoding
Shereef Shehata

2. Introduction

3. A generic block diagram of a perceptual audio encoder
Masking
Thresholds
Time-
Frequency
Analysis
Psychoacoustic
Analysis
Quantization
and
Encoding
Bit-allocation
Entropy
(Lossless)
coding
Parameters MUX
Side
information
Input Audio

4. • The absolute threshold of hearing in a noiseless environment.

5. Table 1.1: Band Edges of 26 Critical Bandwidth Auditory
Fil- ters that Span the Audio Spectrum.
Band No. Bandwidth(Hz) Band No. Bandwidth(Hz)
1 - 100 14 2000-2320
2 100-200 15 2320-2700
3 200-300 16 2700-3150
4 300-400 17 3150-3700
5 400-510 18 3700-4400
6 510-630 19 4400-5300
7 630-770 20 5300-6400
8 770-920 21 6400-7700
9 920-1080 22 7700-9500
10 1080-1270 23 9500-12000
11 1270-1480 24 12000-15500
12 1480-1720 25 15500-25000
13 1720-2000 26 25000-

6. Noise Masking Tone

7. Tone Masking Noise

8. Non-simultaneous masking properties of the human ear

9. The ISO/MPEG-1 Layer III (MP3) encoder

10. Analysis Subband Filter Bank

11. A uniform 32-band critically sampled analysis-synthesis filter bank.
32
+
H0(z)
H1(z)
H2(z)
H31(z)
G0(z)
G1(z)
G2(z)
G31(z)
32
32
32 32
32
32
32
s(n) sout(n)
v0(n) y0(n)
v0(n)
v0(n)
v0(n)
y1(n)
y2(n)
y31(n)
w0(n)
w1(n)
w2(n)
w31(n)

12. 0 100 200 300
Time Index (Samples)
(a)
400 500 600
-4
3
2
1
0
-1
-2
-3
4
x 10
4
Amplitude
0 2 4 6 8 10 12
Time Index(Samples)
14 16 18
-0.25
-0.8
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
Amplitude
(b)
0 2 4 6 8 10 12
Time Index(Samples)
14 16 18
-1
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Amplitude
(c)

13. Implementation of the analysis subband Filter Bank
Input 32 audio
samples
Build Input
Sample Vector
x
Window Vector x by
coefficient vector c
(prototype filter)
Calculate Yi ,
i=0 to 63
Compute coefficients
of M
Calculate the 32 subband
samples by matrixing
PCM Audio In
Subband
Samples
Framing

14. : Coefficients of the prototype filter c(n) and h(n).
0 50 100 150 200 250 300 350 400 450 500
-0.04
-0.03
-0.02
0.02
0.03
0.04
c(n)
Sample Index (n) Sample Index (n)
0 50 100 150 200 250 300 350 400 450 500
-0.005
0
0.005
0.03
0.035
0.04
h(n)

15. Composite magnitude responses of all subbands.
0 0.1 0.2 0.3 0.4 0.5
∧
0.6 0.7 0.8 0.9 1
-140
20
0
-20
-40
-60
-80
-100
-120
Hi(∧)c

16. Sample input vector x
50 100 150 200 250 300 350 400 450 500
SampleIndex(n)
-1
-0.8Input,x(n)
-0.2
0
0.2
0.4
0.6
0.8
1

17. Impulse Response of the Window
Window,c(n) 0 50 100 150 200 250 300 350 400 450 500
SampleIndex(n)
-0.04
-0.03
-0.02
0.04
0.03
0.02
0.01
0
-0.01

18. Windowed output vector
0 50 100 150 200 250 300 350 400 450 500
SampleIndex(n)
-0.03
-0.01
-0.02
0
0.01
0.02
0.03
WindowedOutput,z(n)

20. Time domain and Frequency responses of the filter bank. Subbands 0,1 and 31
50 100 150 500200 250 300
Sample Index (n)
350 400 450
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
h0
c(n)
0 0.1 0.2 0.3 0.4 0.5
∧
0.6 0.7 0.8 0.9 1
-100
-80
-60
-40
-20
0
20
H0
c(∧)(dB)
-120
-0.03
0
0.02
-20
0.01
-40
50 100 150 200 250 300 350 400 450 500
-0.02
-0.01
0
0.03
h1
c(n)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-140
-100
-80
-60
20
Hc(∧)(dB)
1
50 100 150 200 250 300
Sample Index (n)
350 400 450 500
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
hc(n)
31
0 0.1 0.2 0.3 0.4 0.5
∧
0.6 0.7 0.8 0.9 1
-100
-80
-60
-40
-20
0
20
Hc(∧)(dB)
31
Sample Index (n) ∧

21. Hybrid Filter Bank

23. Psychoacoustic Model II

24. Analysis SPL
computation
Spreading function and
excitation pattern
Tonality Index
estimation
Input Signal
Calculation of
masking threshold
for each partition
Estimation of JND
and SMR
Pre-echo detection
and window
switching
SMR

25. Idealized critical band filter bank.
0 0.5
x 10
1 1.5
Frequency (Hz)
2 2.5
4

26. Time-aligned input data, and after applying a Hanning window.

27. FFT magnitude of the windowed audio data

28. Unpredictability measure (cw),

29. Energy of threshold partitions (eb)

30. Weighted unpredictability of threshold partitions

31. Spreading functions centered at bands 4, 5, 6 and 7, respectively.

32. Spread energy (ecb),

33. Spread Unpredictability (ctb).

34. Spread unpredictability(ct b),

35. Plot of ct b/ecb

36. Normalized spread unpredictability
(cbb)

37. Tonality index (t bb).

38. SNR of the threshold partitions, and Masked thresholds of the threshold
partitions.

39. Approximate spectral curve for the threshold in quiet

40. Pre-echo example: uncoded castanets

41. Pre-echo example: Tracastanets

42. Window switching state machine.

43. Energy in scalefactor bands

44. Thresholds in scalefactor bands

45. Signal-to-mask ratio in scalefactor bands.

46. MDCT

47. Illustration of the hybrid filter bank.

48. Illustration of the windowsused in the MDCT filter bank:(a) long window,

49. Illustration of the windowsused in the MDCT filter bank:(b) Start window,

50. Illustration of the windowsused in the MDCT filter bank:(c) Stop window,

51. Illustration of the windowsused in the MDCT filter bank:(d) 3 Short window,

52. Illustration of a typical window switching.
0 10 20 30 40 50 60 70 80 90 100
0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Sample Index
Window

53. Alias reduction butterfly for the encoder.
+
Σ
+
+ Σ
-
cs
cs
ca
ca

54. Alias reduction operations for a granule of MDCT data.
8 butterflies
X0
X1
X2
18 samples
X15
X16
X17
X18
X19
X20
X555
X556
X558
X559
X560
X573
X574
X575

55. Bit Allocation, Quantization, and
Coding

56. Simultaneous Masking
SMRNMR
SNR
MASKING THRESHOLD
MINIMUM MASKING THRESHOLD
SoundPressureLevel(dB)
Frequency
CRITICAL NEIGHBORING
BAND BAND
m-1 bits
m bits
m+1 bits

57. Calculation of
Scalefactor
selection
information
Calculation of
maximum
number of
available bits
Reset of iteration
variables
All
spectral
values
zero?
Outer Loop
Calculation of
number of unused
bits
Adjustment of the
size of reservoir
Y
N

58. Implementation of the Outer Loop (Distortion Control)
Calculation of number of bits needed to encode
the scalefactors.
Binary search for quantizer step-size.Binary search for quantizer step-size.
Inner Loop
Calculation of distortion in each scalefactor band.
Save scaling factors of scalefactor bands.
Preemphasis
Amplification of the scalefactor bands that violate
the masking threshold.
All scalefactor bands amplified?
Amplification of all bands within upper limit?
N
At least one band exceeding allowed distortion?
Y
Y
Restore scaling factors
Y
N
N

60. The effect of the variables status and over in the outer loop execution
1 2
Iterations
3
0
5
10
15
20
25
status
over

61. The effect of the variables status and over in the outer loop execution
1 2 3 4 5 6
0
2
4
6
8
over
status
2
Iterations

62. Unquantized MDCT coefficients for a short block
0 100 200 300
Sample Index
400 500
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
Amplitude

63. MDCT coefficients (magnitude) quantized to meet target bit rate 128 kbps.
14
12
10
BIG
tude
8 VALUES
Ampli
6 QUADRUPLES
4 RUN-LENGTH ZEROS
2
0
0 100 200 300 400 500
Sample Index
0 100 200 300
Sample Index
400 500
0
2
4
6
8
14
12
10
Amplitude
BIG
VALUES
QUADRUPLES
RUN-LENGTH ZEROS

64. Illustration of main data organization and encoding scheme
part2_length
region0 region1 region2
bigvalues region count1 rzero
part3_length
part2_3_length
Scalefactor Huffman Code
part2_length
region0
xxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxxxxxx
region0 region1 region2
bigvalues region
region2
count1
0000000000000000
rzero
part3_length
part2_3_length
Scalefactor Huffman Code

65. Illustration of bit usage in the inner loop.
Iteration 1 Iteration 2
Big Values
Count1
rzeros
Bits used to code subregions
Total available bits
1659
1588
1474

66. Illustration of relationship between global_gain and the number of bits required
to encode a granule.
129 130
Global Gain
131
1400
1700
1650
1600
1550
1500
1450
#Bitsused

67. Header
Frame 1
Header
Frame 2
Header
Frame 3
Header
Frame 4
sync
sideinfo1
sync
sideinfo2
sync
sideinfo3
sync
sideinfo4
main data 1
main data 2
main data 3
main data 4
main data 4main data 3main data 2main data 1

68. Illustration of total available bits to encode data frames.
Available Bits
Reservoir Size
Mean Bits
Granule0
Granule0
Granule0
Granule0
Granule0
Granule0
Granule1
Granule1
Granule1
Granule1
Granule1
Granule1
Frame 0 Frame 1 Frame 2 Frame 3 Frame 4 Frame 5

69. Decoder

70. Block Diagram of MP3 decoder

71. Organization of scalefactors and Huffman coded data.
GRANULE 0 GRANULE 1
LEFT CHANNEL RIGHT CHANNEL
SCALEFACTORS HUFFMAN CODE
BITS
RIGHT CHANNEL LEFT CHANNEL
. . . . SCALEFACTORS HUFFMAN CODE
BITS
HEADER
(32)
CRC
(0,16)
SIDE INFORMATION
(136,256)
MAIN DATA ANCILLARY
BITS

72. CRC Error Checking
T212155
+
+ +
DATA BITS
T15 T14 T13 T1 T0
b0b1b2b13b15 b14
CRC check diagram.

73. Alias reduction butterfly for the decoder
+
Σ
-
+ Σ
+
cs
cs
ca
ca

74. 36 samples
0…35
WINDOWED
OUTPUT FROM
IMDCT
0…17 18…35
SAVED FROM
PREVIOUS
GRANULE
18 samples
+
ADD FIRST HALF
18 samples
SAVE SECOND HALF
18 samples
RESULT

75. Polyphase implementation of the synthesis filter bank
31
63
V FIFO
16 V vector FIFO
(1024 samples)
0
IMDCT
0
V vector
U vector
511
D window
511
511
31
0
+ + + +
31
0
=
Reconstructed
samples
Subband
samples
W vector