Laboratory 2 Sound Spectrum Analysis

1
Laboratory 2Sound Spectrum Analysis

• Introduction
• A. Concept of a Filter
• 1. Definition
• 2. Contiguous Filter
• 3. Band-Spectrum
• B. Octave Filter
• 1. Definition
• 2. Contiguous
• 3. Octave-Band Spectrum
• 4. 1/3 and 1/12 - Octave Filters
• C. Incorporation into SLM
• II. Exercises

2
Filters
Filter Device whose gain is a function of
frequency
Gain
G
, Nominal Gain
o
0.707G
o
Bandwidth
Frequency
f
f
Upper
L
f
U
Lower
c
Cutoff
Cutoff
Center
Frequency
Frequency
Frequency
3
Filters
Contiguous Filters Filters with contiguous
upper and lower cutoff frequencies and equal
nominal gains
4
Filters
1
1
G
o
0.707G
o
Frequency
2
2
G
o
The (four) filtered signals, when combined
correctly will produce the unfiltered signal
0.707G
o
r
Frequency
3
3
Frequency
4
G
o
0.707G
4
o
Frequency
5
Filters
o
Signals
Passed
Signals
Rejected
i
t
a
R

e
d
u
t
i
l
p
Signals
Signals
f
m
a) Low pass filter
A
Passed
Rejected
o
Signals
Signals
Signals
i
f
t
a
b) High pass filter
Passed
Rejected
Rejected
R

e
d
u
t
i
l
p
m
f
A
c) Band pass filter
6
Filters
a) Input square wave spectrum
....
3f
5f
f
Frequency
1
1
1
b) Bandpass filter frequency
response
c) Filter output
Bandpass filter response to a square

wave input
7
Filters - Constant Bandwidth vs.Constant
Bandwidth
Linear Frequency Scale
Constant Percentage
Constant Bandwidth
Bandwidth
Relative
0.1 1 2 3 4
5 6 7 8
9 10
Frequency
Highest decade
Next highest decade
8
Filters - Constant Bandwidth vs.Constant
Bandwidth
Logarithmic Frequency Scale
9
Octave Filter
The Octave Filter
Bandwidth
Gain
1000 2
Octave Filter Bandwidth about 70 of the
Center Frequency
1.0
.707
1000
1000
1000 2
Center
2
Frequency
10
Third - Octave Filter
Third Octave
Gain
Octave Filter
Filter
G
o
The basic Octave-Filter is divided into
.707G
3 equal parts on logarithmic scale
o
f (log)
f
c
1/3
x
f
f
2


f
f

c
L
c
H
11
Third - Octave Filter
Third-Octave Filter Bandwidth about 23 of
the Center Frequency
Center Frequency (Hz)
50 100 200 400 800 1600 3150
6300 12600
63 125 250 500 1000 2000 4000
8000 16000
80 160 315 630 1250 2500 5000
10000 20160
BW of 1/12th Octave about 6 of the Mean
Frequency
1/24th Octave about 3 of the Mean Frequency
12
Octave - Band Filter Set
GAIN
1

500
1000
1000 2
2000Hz
1000
2
13
Octave - Band Analysis
Bar Form
31.5 63 125 250 500
1000 2000 4000 8000 16000
Octave Band Center Frequency, Hz
14
Octave - Band Analysis
Alternate Form
Hz
31.5 63 125 250 500
1000 2000 4000 8000 16000
15
Linear Amplitude Scale
Linear Frequency ? Easy Identification of
Harmonics Side Bands ? Good
Resolution at Higher Frequencies ?
Frequency Range Limited to 1.5
Decades
1.0
0.5
0
16
Log Amplitude Scale
Log Frequency ? Can be used across Broad
Frequency Range ? Approximates Human
Perception ? Speed Compensation Simple ? Certain
Relationships Easy to
Evaluate ? Poor Resolution at Higher
Frequencies
0
- 20
- 40
- 60
- 80
17
Combining Levels
3
2.5
2
1.5
CORRECTION TO BE ADDED TO HIGER LEVEL
1
0.5
0
0
1
2
3
4
5
6
7
8
9
10
DIFFERENCE IN DECIBELS BETWEEN TWO LEVELS BEING
ADDED
Add correction to the higher level to obtain
combined level