Discrete and Digital Signals and Systems - Digital Signal Processing: An Introduction with MATLAB and Applications - page 126

Time

Direct
sound

Echoes Reverberations

x ( n ) x ( n )

Direct sound

H e ( z )

Equalizer Listener

y ( n )

A bank of echo filters

s ( n )

c ( n )
Audio source

A bank of reverb filters

Fig. 2.43 Audio effects. Above an audio signal and its reflections in a listening venue. Below
simulation of specific acoustics in another venue

Figure ( 2.41 ) shows a block diagram of a DC blocker, while Fig. ( 2.42 ) shows
its practical performance with sinusoidal dc-shifted signals. It is evident that this
performance is dependent on how close a is to 1. When a = 0.99, the filter
removes the DC from the (low-frequency) 20 Hz sinusoid, but it also introduces a
phase change and an attenuation.

2.6.9.6 An Application of FIR / IIR Digital Filters: Simulation of Acoustic
Effects

A piece of music played in a concert hall does not sound the same as if it is played
in a living room. This is due to the echoes (early reflections) and the reverberations
(late reflections) which vary from setting to setting. One can actually simulate a
concert hall in a living room using the following steps:

1. Equalize the audio transfer function of the room, H r (z). That is, eliminate any
special effects that the living room is inherently creating. This is done by first
sending an audio impulse d(n), and then measuring the impulse response h r (n).
The transfer function is then given by H r (z) = fft{h r (n)}. Then one designs an
equalizing filter H e (z) = 1/H r (z), with say the Remez algorithm.
2. Simulate the echoes and the reverberations as follows:

• For echoes: y(n) = x(n) ? ax(n - N). This is so because an echo is a direct
reflection of the delayed input signal. Hence, H(z) = 1 ? az -N . This is an
FIR filter. In practice, choose NT s C 0.05