Download unit4 - University of Kentucky College of Engineering

EE513
Audio Signals and Systems
Noise
Kevin D. Donohue
Electrical and Computer Engineering
University of Kentucky
Quantization Noise
Signal amplitudes take on a continuum of
values. A discrete signal must be digitized
(mapped to a finite set of values) to be
stored and processed on a computer/DSP
Analog Signal
Discrete-time
Signal
Digital Signal
Coder
Quantizer
xa (nT )
xˆ (n)
xˆ (nT )
11
10
01
00
Quantization Error and Noise
xa (t )
Analog
xa (nT )
ˆ
Discrete x(nT )
Digital
 Quantization has the same effects as adding noise to the signal as long
as the rounding error is small compare to the original signal amplitude:
 q (nT )  xa (nT )  xˆ (nT )
xa (nT )   q (nT )  xˆ (nT )
 Intervals between quantization levels are proportional to the
resulting quantization noise since they limit the maximum rounding or
truncation error.
For uniform quantization, the quantization level interval is the
maximum signal range divided by the number of quantization
intervals.
11
10
01
00
Quantization Noise
Original CD clip quantized at 16 bits (blue)
Quantized at 6 bits (red)
Quantized at 3 bits (black)
PSDs of Quantized Signal; Song -Tell Me Ma
20
0
3 bit
dB
-20
6 bit
-40
-60
-80 1
10
16 bit
10
2
3
10
Hertz
10
4
10
5
Quantization Noise Analysis
Assume  q (n ) is a uniformly distributed (amplitude),
white, stationary process that is uncorrelated with the
signal.
• Show that the signal to quantization noise ratio (SNRq)
for a full scale range (FSR) sinusoid, quantized with B bit
words is approximately:
SNR q  6 B  1.8 dB
• Note this is the SNR for a signal amplitude at FSR,
signals with smaller amplitudes. What would be the
formula for a sinusoid with an X% FSR?
Homework 4.1
• Derive a formula for SNRq similar to the one
on last slide (in dB) for a sinusoid that is X%
of the FSR in amplitude.
Room Noise
Noise generated from a source inside a room will undergo frequency
dependent propagation, absorption and refection before reaching the sink.
Thus, the room effectively filters the sound.
Sound impinging on surfaces in the room will be absorbed, reflected, or
diffused.
Absorption
Reflection
Diffusion
Heat
Transmission
Direct
Sound
Specular
Reflected
Sound
Direct
Sound
Diffuse
Scattered
Sound
Direct
Sound
Reflection Absorption Effects
Reflected and reverberant sounds become particularly bad
distractions because they are highly correlated with the original
sound source. The use of absorbers and diffusers on reflective
surfaces can cut down the reverberation effects in rooms.
The model for a signal received at a point in space from many
reflections is given as:
N 
r (t )     n ( ) s(  (t   n )) d
n 1 0
where n(t) denotes the attenuation of each reflected signal due to
propagation through the air and absorption at each reflected
interface and n is the time delay associated with the travel path from
the source to the receiver. The signal in the frequency domain is
given by:
N
R( f )  S ( f )  n ( f ) exp(  j 2f n )
n 1
Reverberant Sound Travel
RF1
EF1
EF2
S
D
L
RF2
EF3
EF4
RF3
The near or direct field (D)
The free or early field (EF1 and EF2)
The reverberant or diffuse field (RF1 to RF3)
Decay of Reverberant Sound Field
Sound Level
Direct Sound
Reverberation
60 dB
Time
Initial Time Delay Gap
Reverberation Time
The time it takes for the reverberant sound field to decay
by 60dB has become a standard way to characterize
reverberation in room acoustics.
Room Reverberation Time
For a space with many randomly distributed reflectors
(typically large rooms) reverberation time (RT60 ) is
defined as the amount of time for the sound pressure in a
room to decrease by 60 dB from its maximum. The time
is statistically predicted from the room features with the
Sabine equation:
RT 60( f )  .161
V
N
 S a ( f )  4m( f )V
i i
i 1
where
 V is the volume of the room in cubic meters
 Si is the surface area of the ith surface in room (in square meters)
 ai is the absorption coefficient of ith surface
 m is the absorption coefficient of air.
Discuss: The relationship between absorption, volume, and RT.
Room Response to White Noise Input
Data collected and spectrogram computed by H.L. Fournier
Note frequency dependence on of decay time.
Example
Given the simulated reverb signal compute the RT60. Find the
autocorrelation function and try to estimate the delays associated with
the major scatterers.
% Create reverb signal
[y,fs] = wavread('clap.wav'); % Read in Clap sound
% Compute autocorrelation function of envelop and look for peaks
% to indicate delay of major echoes
% Apply simulated reverb signal
maxlag = fix(fs*.5);
yout1 = mrevera(y,fs,[30 44 121]*1e-3,[.6 .8 .6]);
[ac, lags] = xcorr(env-mean(env), maxlag);
taxis = [0:length(yout1)-1]/fs;
figure(2)
% Compute envelope of signal
plot(lags/fs,ac)
env = abs(hilbert(yout1));
xlabel('seconds')
figure(1)
ylabel('AC coefficient')
plot(taxis,20*log10(env+eps)) % Plot Power over time
% Compute autocorrelation function of raw and look for peaks to
hold on
% indicate delay of major echoes
% Create Line at 60 dB below max point and look for
intersection point
[ac, lags] = xcorr(yout1, maxlag);
mp = max(20*log10(env+eps));
plot(lags/fs,ac)
mp = mp(1);
xlabel('seconds')
dt = mp-60;
ylabel('AC coefficient')
plot(taxis,dt*ones(size(taxis)),'r'); hold off; xlabel('Seconds')
ylabel('dB'); title('Envelope of Room Impulse Response')
figure(3)
Room Modes
The air in a (small) rectangular room has natural modes of
vibration given by:
2
2
c  p  q   r 
f 
     
2  L  W   H 
2
where c is the speed of sound in the room p, h, and r are
integers 0,1,2, …., and L, W, and H are the length, width,
and height of the room.
Amplifiers and Distortion
Efficiency – Output power over Input power (including that of the
power supply).
Distortion – Total harmonic distortion (THD). For a sinusoidal
signal input, THD is the ratio of power at all harmonic frequencies
Pi (excluding the fundamental P1) to the power at the fundamental
frequency.

THD 
P
i 2
P1
i
PT  P1

P1
where PT is total signal power
Fidelity – Flatness of frequency response characterized by
frequency range and transfer function variation in that range.
Example
Given the transfer characteristic for a class B amplifier
below, compute the THD for a 3 volt input sinusoid.
Vout
7v
-3v
-0.6v
Vin
0.6v
-7v
3v
Amplifier Classes
Class A - Low distortion, bad efficiency. Output stage
with single transistor requires DC biased output (10-20%
efficiency).
Class B - Crossover distortion, good efficiency. Output
stage has 2 transistors so bias current is zero (~80%
efficient).
Class AB – Reduced crossover distortion, good
efficiency. Output stage has 2 transistors with biasing to
push signal out of crossover distortion range.
Class D – Moderate distortion, high efficiency, operates
in switch mode. Good for battery driven applications.
Center Clip Distortion
3
Original
Distorted
amplitude
2
1
0
-1
-2
-3
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
seconds
Harmonic Peak Heights = [-8, -23, -29, -37, -47, -55, -47, -46, -49, -57];
0
Original
Distorted
-20
1023/10  1029 /10  1037 /10    1057 /10
THD 
108 /10
-40
dB
fo = 200 Hz
THD = 4.13%
-60
-80
-100
0
500
1000
1500
2000
Hz
2500
3000
3500
4000
Example
Given the transfer characteristic for a class AB amplifier
below, compute the THD for a 3 volt input sinusoid.
7v
Vout
-3v
-1.75v
Vin
1.75v
3v
-7v
Clip/Overload Distortion
3
Original
Distorted
amplitude
2
1
0
-1
-2
-3
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
seconds
Harmonic Peak Heights = [-7, -21, -46, -37, -44, -49, -45, -72, -49, -55];
0
Original
Distorted
-20
10 21/10  10 46 /10  10 37 /10    1055 /10
THD 
107 /10
fo = 200 Hz
THD = 4.14%
dB
-40
-60
-80
-100
0
500
1000
1500
2000
Hz
2500
3000
3500
4000