Frequency analysis
Sound spectrum
The sound spectrum is a chart of SPL vs frequency.
Simple tones have spectra composed by just a small number of
“spectral lines”, whilst complex sounds usually have a “continuous
spectrum”.
a)
Pure tone
b)
Musical sound
c)
Wide-band noise
d)
“White noise”
Time-domain waveform and spectrum:
a)
Sinusoidal waveform
b)
Periodic waveform
c)
Random waveform
Analisi in bande di frequenza:
A practical way of measuring a sound spectrum consist in employing
a filter bank, which decomposes the original signal in a number of
frequency bands.
Each band is defined by two corner frequencies, named higher
frequency fhi and lower frequency flo. Their difference is called the
bandwidth Df.
Two types of filterbanks are commonly employed for frequency
analysis:
• constant bandwidth (FFT);
• constant percentage bandwidth (1/1 or 1/3 of octave).
Constant bandwidth analysis:
“narrow band”, constant bandwidth filterbank:
• Df = fhi – flo = constant,
for example 1 Hz, 10 Hz, etc.
Provides a very sharp frequency resolution (thousands of bands),
which makes it possible to detect very narrow pure tones and get
their exact frequency.
It is performed efficiently on a digital computer by means of a well
known algorithm, called FFT (Fast Fourier Transform)
Constant percentage bandwidth analysis:
Also called “octave band analysis”
• The bandwidth Df is a constant ratio of the center frequency of
f c  f hi  f lo
each band, which is defined as:
•
Df
1

 0.707
fc
2
fhi = 2 flo
1/1
octave
•
Df
 0.232
fc
fhi= 2 1/3 flo
1/3
octave
Widely employed for noise measurments. Typical filterbanks
comprise 10 filters (octaves) or 30 filters (third-octaves),
implemented with analog circuits or, nowadays, with IIR filters
Nominal frequencies for octave and 1/3 octave bands:
•1/1 octave bands
•1/3 octave bands
Octave and 1/3 octave spectra:
•1/3 octave bands
•1/1 octave bands
Narrowband spectra:
• Linear frequency axis
• Logaritmic frequency axis
White noise and pink noise
• White Noise:
Flat in a narrowband
analysis
• Pink Noise:
flat in octave or 1/3
octave analysis
Critical Bands (BARK):
The Bark scale is a psychoacoustical scale proposed
by Eberhard Zwicker in 1961. It is named
after Heinrich Barkhausen who proposed the first
subjective measurements of loudness
Bark
N.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Center freq.
50
150
250
350
450
570
700
840
1000
1170
1370
1600
1850
2150
2500
2900
3400
4000
4800
5800
7000
8500
10500
13500
LoFreq
0
100
200
300
400
510
630
770
920
1080
1270
1480
1720
2000
2320
2700
3150
3700
4400
5300
6400
7700
9500
12000
HiFreq
100
200
300
400
510
630
770
920
1080
1270
1480
1720
2000
2320
2700
3150
3700
4400
5300
6400
7700
9500
12000
15500
Bandwidth
100
100
100
100
110
120
140
150
160
190
210
240
280
320
380
450
550
700
900
1100
1300
1800
2500
3500
Third
octave bands
Terzi d'ottava
N.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Center freq.
25
31.5
40
50
63
80
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000
5000
6300
8000
10000
12500
16000
20000
LoFreq
22
28
35
45
56
71
89
112
141
179
224
281
355
447
561
710
894
1118
1414
1789
2236
2806
3550
4472
5612
7099
8944
11180
14142
17889
HiFreq
28
35
45
56
71
89
112
141
179
224
281
355
447
561
710
894
1118
1414
1789
2236
2806
3550
4472
5612
7099
8944
11180
14142
17889
22361
Bandwidth
6
7
9
11
15
18
22
30
37
45
57
74
92
114
149
184
224
296
375
447
570
743
922
1140
1487
1845
2236
2962
3746
4472
Critical Bands (BARK):
ampiezzeof
di banda
- Bark
vs. 1/3
1/3 Octave
Comparing theConfronto
bandwidth
Barks
and
octave bands
10000
Bandwidth (Hz)
1000
Barks
Bark
Terzi
100
1/3 octave bands
10
1
10
100
1000
Frequenza (Hz)
10000