EE513Audio Signals and Systems

NoiseKevin D. DonohueKevin D. Donohue

Electrical and Computer EngineeringUniversity of KentuckyUniversity of Kentucky

Quantization NoiseSignal amplitudes take on a continuum of values A discrete signal must be digitizedvalues. A discrete signal must be digitized (mapped to a finite set of values) to be stored and processed on a computer/DSPp p

Digital SignalDiscrete-time SignalAnalog Signal )(ˆ nxSignal

QuantizerAnalog Signal

Coder

11

)(nTxa )(ˆ nTx

)(nx

11 10 01 00

Quantization Error and Noise)(txa )(nTxa )(ˆ nTxAnalog Discrete Digital

11 10 01 00

Analog Discrete Digital

Quantization has the same effects as adding noise to the signal:

)(ˆ)()( nTxnTxnT aq )(ˆ)()( nTxnTnTx qa Intervals between quantization levels are proportional to the resulting quantization noise since they limit the maximum rounding orresulting quantization noise since they limit the maximum rounding or truncation error.

For uniform quantization, the interval between signal levels is the maximum signal amplitude value divided by the number of quantization intervals.

Quantization NoiseOriginal CD clip quantized at 16 bits (blue) Quantized at 6 bits (red)Quantized at 6 bits (red)Quantized at 3 bits (black)

PSD f Q ti d Si l S T ll M M

0

20PSDs of Quantized Signal; Song -Tell Me Ma

3 bit

-40

-20

dB 6 bit

80

-60

40

16 bit

101 102 103 104 105-80

Hertz

Quantization Noise AnalysisAssume is a uniformly distributed (amplitude), white stationary process that is uncorrelated with the

)(nqwhite, stationary process that is uncorrelated with the signal.

• Show that the signal to quantization noise ratio (SNRq) for a full-swing range (FSR) sinusoid, quantized with Bbit words is approximately:bit words is approximately:

dB 8.16SNR q B

Room NoiseNoise 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 DiffusionAbsorption Reflection Diffusion

HeatTransmission

DirectSound

DirectSoundSpecular

R fl t d

DirectSound

DiffuseScattered

SoundReflectedSound

Reflection Absorption EffectsReflected 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

nnn dtstr

1 0

))(()()(

where n(t) denotes the attenuation of each reflected signal due to propagation through the air and absorption at each reflected i t f d i th ti d l i t d ith th t l th finterface 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

n

nn fjffSfR1

)2exp()()()(

Reverberant Sound TravelEF1

RF1

LS

EF2

RF2D

EF3

EF4 RF3

The near or direct field (D)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

Direct Sound

Leve

lSo

und

L

Reverberation60 dB

TimeInitial Time Delay Gap Reverberation Time

The time it takes for the reverberant sound field to decayby 60dB has become a standard way to characterizeby 60dB has become a standard way to characterize reverberation in room acoustics.

Room Reverberation TimeFor 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

t d b 60 dB f it i Th tiroom to decrease by 60 dB from its maximum. The time is statistically predicted from the room features with the Sabine equation:

VffS

VfRT N)(4)(

161.)(60

where V is the volume of the room in cubic meters

VfmfaSi

ii )(4)(1

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 FournierData collected and spectrogram computed by H.L. FournierNote frequency dependence on of decay time.

Examplei h i l d b i l h i d hGiven 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

% Apply simulated reverb signal

yout1 = mrevera(y fs [30 44 121]*1e-3 [ 6 8 6]);

% Compute autocorrelation function of envelop and look for peaks % to indicate delay of major echoes

maxlag = fix(fs*.5);

[ac, lags] = xcorr(env-mean(env), maxlag);yout1 = mrevera(y,fs,[30 44 121] 1e-3,[.6 .8 .6]);

taxis = [0:length(yout1)-1]/fs;

% Compute envelope of signal

env = abs(hilbert(yout1));

figure(2)

plot(lags/fs,ac)

xlabel('seconds')

l b l('AC ffi i t')figure(1)

plot(taxis,20*log10(env+eps)) % Plot Power over time

hold on

% Create Line at 60 dB below max point and look for

ylabel('AC coefficient')

% Compute autocorrelation function of raw and look for peaks to

% indicate delay of major echoes

[ac, lags] = xcorr(yout1, maxlag);% C eate e at 60 d be ow a po t a d oo ointersection point

mp = max(20*log10(env+eps));

mp = mp(1);

dt = mp-60;

figure(3)

plot(lags/fs,ac)

xlabel('seconds')

ylabel('AC coefficient')dt mp 60;

plot(taxis,dt*ones(size(taxis)),'r'); hold off; xlabel('Seconds')

ylabel('dB'); title('Envelope of Room Impulse Response')

ylabel( AC coefficient )

Room ModesThe air in a (small) rectangular room has natural modes of vibration given by:

222

2

Hr

Wq

Lpcf

where c is the speed of sound in the room p, h, and r are

2 HWLf

p pintegers 0,1,2, …., and L, W, and H are the length, width, and height of the room.

Amplifiers and DistortionEfficiency – 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 ffrequency.

12

PPP

P

PTHD Ti

i

where PT is total signal power

l f f h i d b

11 PP

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.

Vout7v

Vin-0.6v

-3v in

0.6v3v

-7v

Amplifier ClassesClass A - Low distortion, bad efficiency. Output stage with single transistor requires DC biased output (10-20% efficiency)efficiency).

Class B - Crossover distortion, good efficiency. Output stage has 2 transistors so bias current is zero (~80%stage has 2 transistors so bias current is zero (~80% efficient).

Class AB Reduced crossover distortion goodClass 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 Distortion3

1

2

3

tude

OriginalDistorted

-2

-1

0am

plit

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-3

seconds

Harmonic Peak Heights = [-8, -23, -29, -37, -47, -55, -47, -46, -49, -57];

-40

-20

0

OriginalDistorted

f 200

10/8

10/5710/3710/2910/23

1010101010

THD

-80

-60

dB fo = 200 HzTHD = 4.13%

0 500 1000 1500 2000 2500 3000 3500 4000-100

Hz

Example Given the transfer characteristic for a class AB amplifier below, compute the THD for a 3 volt input sinusoid.

Vout7v

V-3v

-1.75v Vin

3v1.75v

1.75v

-7v

Clip/Overload Distortion

1

2

3

ude

OriginalDistorted

-2

-1

0

ampl

itu

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-3

seconds

Harmonic Peak Heights = [-7, -21, -46, -37, -44, -49, -45, -72, -49, -55];

-40

-20

0 OriginalDistorted

f = 200 Hz

10/7

10/5510/3710/4610/21

1010101010

THD

-80

-60

dB

fo 200 HzTHD = 4.14%

0 500 1000 1500 2000 2500 3000 3500 4000-100

Hz