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Noise Analysis
Citation preview
AcousticsAcoustics
Dr. Tamer Elnady – Dr. Wael Akl – Dr. Adel [email protected]
Signal Analysis & Measurement Techniques
Signal Analysis in Time Domain (cont’d)
tttpffpp
5sin3.02sin1Hz 5.2 , Hz 1Pa 3.0ˆ , Pa 1ˆ
21
21
0 1 2 3 4 5-2
-1
0
1
2
t(s)
p(Pa
)
tfptfptp 2211 2sinˆ2sinˆ
Fourier Analysis
Any Periodic Signal can be considered a sum of a number of harmonic componentsPeriodic Signals are very common in Real life
)()( nTtptp
N
nnn tnfptp
10 )2cos(ˆ)(
Fourier Analysis
Any Periodic Signal can be considered a sum of a number of harmonic componentsPeriodic Signals are very common in Real life
)()( nTtptp
N
nnn tnfptp
10 )2cos(ˆ)(
Two Sine waves
0 0.01 0.02 0.03 0.04 0.05
Time [s]
0 50 100 150 200
Frequency [Hz] a) b)
Amplitude Signal
Fourier Analysis
0 0.05 0.1 0.15 0.2 0.25 0.3
Time [s]
0 20 40 60 80 100
Frequency [Hz] a) b)
Signal Ampl
Fourier Analysis
Tid [s]
Frekvens [Hz]b)a)
Signal Amp
Frekvens [Hz]Tid [s]a) b)
Signal Amp
t(s)Time [s]
Time [s]
Frequency [Hz]
Frequency [Hz]
Fourier Analysis
11
0 )sin()cos()(n
onn
on tntnta
2
2
2
2
22
20 )(111)(
T
T
T
T
T
T
dttaT
dtdtta
2
20
2
20
22
20 )cos()(2)(cos)cos()(
T
T
T
T
T
Tn dttnta
Tdttndttnta
2
20
2
20
22
20 )sin()(2)(sin)sin()(
T
T
T
T
T
Tn dttnta
Tdttndttnta
Fast Fourier Transform (FFT)
t(s)
Assignment: Read the MATLAB help about the fft function.[put website!!]
Types of Filters
1
frekvens
Amplitud
Förstärkning
f
(i)
(ii)
(iii)
(iv)
f
f
f
A
f
A
f
A
f
A
f
Förstärkning
Förstärkning
Förstärkning
1
1
1
Amplitude
Frequency
Amplification
Amplification
Amplification
AmplificationLow pass
High pass
Pass band
Stop band
Band Pass Filters
Amplification [dB] Amplification [dB]
0 0
-3
f f Frequency
B=f -f
a) b) l u
u l
f f l u
Band width,
Frequency
Addition of Uncorrelated Sound Fields
Proof of this in sheet 1, problem 2
N
n
Lp
pn
totL
1
1010log10
Narrow band vs. Octave bands
Octave band
Third octave band
Narrow band
frequency (log) [Hz]
L [dB] p