Echo Generationand

Simulated Reverberation

R.C. Maher

ECEN4002/5002 DSP Laboratory

Spring 2003

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 2

Recirculating Delay Line

• Recall that a simple delay FIFO (first-in, first-out) queue can be implemented using a modulo buffer

• Now, consider a recirculating buffer:+

Delay Line (z-N)k

output can also be taken here

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 3

Recirculating Delay (cont.)

+

Delay Line (z-N)k

x[n] y[n]

kz

z

kzzX

zY

zYkzzXzY

N

N

N

N

−=

−=

+=

−

−

11

)()(

)()()( N poles equally spaced

around circle (radius k1/N)

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 4

Recirculating Delay (cont.)• Example: unit sample response (N=8, k=0.8)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 8 16 24 32 40 48 56 64 72 80 88 96

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 5

Recirculating Delay (cont.)• Frequency response of system

• A “comb” filter

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5

Normalized Frequency (/fs)

Magnitude (linear scale)

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 6

Echo Generator

• If length N is short, comb filter effect (audio coloration) is noticeable

• If length N corresponds to a time delay of 200ms or more, output perceived as an echo of the input

• Scaling of input is typically needed to prevent overflow

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 7

Acoustics

• Sound propagates through air as a longitudinal wave

• Speed of sound:– 343 m/s @ 20°C (331 m/s @ 0°C)– About 1125 ft/s– About 1 ft/ms (light travels about 1 ft/ns)– About 5 seconds per mile

• Audible wavelengths: 1.7cm to 17m

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 8

Human Hearing Characteristics• Frequency sensitivity roughly 20 Hz – 20kHz

– 3 decades, or 10 octaves– Compares to less than one octave for human visual system

(wavelengths: 3800 – 7600 angstroms)

• Amplitude sensitivity roughly 20Pa – 20Pa– Atmospheric pressure: 105 Pa– Minimum audible sound corresponds to motion a fraction

of diameter of hydrogen atom!– Any better, and we would “hear” thermal noise

• Difference judgments good, absolute judgments poor

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 9

Acoustical Transfer Function

• Linear Time-Invariant (LTI) systems can be fully described by an impulse response

• Fourier Transform of the impulse response is the transfer function

• Acoustical path from a sound source to the listener’s ear is LTI, so we can describe the acoustical system with a transfer function

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 10

Reflections and Reverberation

• Direct sound arrival is followed by reflections from room surfaces

• Overlapping reflections are heard as reverberation

• Direct-to-Reverberant ratio gives cues to size of room, type of room surfaces, and distance from source

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 11

Direct Sound and Reflections

Sound Source

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 12

Reverb Simulation

• Method 1: obtain impulse response of real room, then convolve with input signal– Results can be good, but computation and

storage requirements are high: impulse response sequence for 3-5 seconds is ~200k

• Method 2: use recirculating delay lines to create an artificial impulse response– Less computation and storage, but tricky to get

satisfactory sound quality

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 13

Reverb Simulation (cont.)

• For good reverb:– echo density (echoes per second) must increase

as time goes on– response should be quasi-random (no spectral

coloration)– high frequencies typically decay faster than low

frequencies

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 14

Reverb Simulation (cont.)

• Plan: use parallel recirculating delay lines with incommensurate delays

+ Delay Line (z-N1)

k1

+

+ Delay Line (z-N2)

k2

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 15

Other Improvements

• Cascade of all pass recirculators

+ Delay Line (z-N)

k

+

-k

N

N

kz

zkzH −

−

++

=1

)(

N poles and zeroes equally spaced around

circle(pole radius k1/N, zero radius k-1/N)

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 16

Other Improvements (cont.)

• Add lowpass filter to feedback path: shortens high frequency reverb time: more like natural reverberation

+ Delay Line (z-N)

kLPF

ECEN4002 Spring 2003 Echo and Reverb R. C. Maher 17

EVM Note: External Memory

• To use external memory on EVM, need to program the bus control register and the address attribute register 0 (see 56300 Family Manual)movep #$040821,x:M_AAR0 ;Compare 8 most significant bits

;Look for a match with address ;Y:0000 0100 xxxx xxxx xxxx xxxx

;No pack, no mux, Y enabled ;P and X disabled

;AAR0 pin active lowmovep #$012421,x:M_BCR ;One ext. wait state

• Access to external memory is slower than internal memory: wait state stalls processor