Review of dsp fundamentals

So far:

• So far:
• Historical overview of speech technology basic components/goals for systems
• Quick review of DSP fundamentals
• Quick overview of pattern recognition basics

• Next talk focuses on the nature of the signal:
• Acoustic waves in small spaces (sources)
• Acoustic waves in large spaces (rooms)

Acoustic waves - a brief intro

• A way to bridge from thinking about EE to thinking about acoustics:
• Acoustic signals are like electrical ones, only much slower …
• Pressure is like voltage
• Volume velocity is like current (and impedance = Pressure/velocity)
• For wave solutions, c is a lot smaller
• To analyze, look at constrained models of common structures: strings and tubes

• +

• x + dx

• =

• So 2y 2y

• x2

• t2

• c2

• is the wave equation for transverse vibration on a string

• Where c can be derived from the properties of the medium, and is the wave propagation speed

• =

• Solutions dependent on boundary conditions
• Assume form f(t - x/c) for positive x direction
• Then f(t + x/c) for negative x direction
• Sum is A f(t - x/c) + B f(t +x/c)

• L

• x

• 0

• Open end

• Excitation

• Uniform tube, source on one end, open on the other

• c = f

• Plane wave propagation for frequencies below ~4000 Hz

• By looking at the solutions to this equation, we can show that c is the speed of sound

• t +

• +

• =

• 2

• 2

• ..

• +

• u(0,t) = ej t = A e j(t - 0/c) - B e j(t + 0/c)

• + -

• +

• -

• +

• +

• -

• Let u+(t - x/c) = A e j(t - x/c) and u-(t + x/c) = B e j(t + x/c)

• e jt

u(0,t) = ej t = A e j(t - 0/c) - B e j(t + 0/c)

• Now you can get equation 10.24 in text, for excitation U() ej t :

• p(L,t) = 0 = A e j(t - L/c) + B e j(t + L/c)

• Problem: Find A and B to match boundary conditions

• Solve for A and B (eliminate t)

• u(x,t) = cos [(L-x)/c] U() ej t

• cos [(L)/c]

• Poles occur when:

•  = (2n + 1)πc/2L

• f = (2n + 1)c/4L

• (upcoming homework problem)

• c = 340 m/s L = 17cm 4L = .68 m

• f1

First 3 modes of an acoustic tube open at one end

Effect of losses in the tube

• Upward shift in lower resonances
• Poles no longer on unit circle - peak values in frequency response are finite

Effect of nonuniformities in the tube

• Impedance mismatches cause reflections
• Can be modeled as a succession of smaller tubes
• Resonances move around - hence the different formants for different speech sounds

• =

• =

Acoustic reverberation

• Reflection vs absorption at room surfaces
• Effects tend to be more important than room modes for speech intelligibility
• Also very important for musical clarity, tone

• =

• =

• =

• +

• +

• 4

• (uniformly distributed and diffuse)

• =

• =

• -

• Decay of intensity
• when source is shut off (W=0)

• =

• =

• =

• =

• -

• 4mV

• =

• The phrase “two oh six” convolved with impulse
• response from .5 second RT60 room

• Initial time delay gap = t0

Measuring room responses

• Impulsive sounds
• Correlation of mic input with random signal source (since R(x,y) = R(x,x) * h(t) )
• Chirp input
• Also includes mic, speaker responses
• No single room response (also not really linear)

Effects of reverb

• Increases loudness
• “Early” loudness increase helps intelligibility
• “Late” loudness increase hurts intelligibility
• When noise is present, ill effects compounded
• Even worse for machine algorithms

Dealing with reverb

• Microphone arrays - beamforming
• Reducing effects by subtraction/filtering
• Stereo mic transfer function
• Using robust features (for ASR especially)
• Statistical adaptation

Artificial reverberation

• Physical devices (springs, plate, etc.)
• Simple electronic delay with feedback
• FIR for early delays (think of “initial time delay gap” in concert halls), IIR for later decay
• Explicit convolution with stored response