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\lhead{\bfseries EE 451}
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\begin{center} 
{\bf EE 451 } \\[.1in]
{\large \bf Lab 11:  Simple Audio Effects}\\[0.2in]
\end{center}

``Reverberation'' is an interesting sound effect which can be generated
easily with the 56002.  A simple reverb is an echo, generated by adding
a delayed output signal to  the input signal:

$$y(n) = x(n) + \alpha y(n-D)$$


where $\alpha$ is a constant (say, 0.5), and $D$ is large enough to produce
delays of, say, 50 ms to 500 ms.  

An echo generated using Equation 1 has a disadvantage in that the
frequency response is not flat -- i.e., some frequencies will be enhanced over
others.  This can be fixed using an equation of the form


$$ y(n) = \alpha x(n) + x(n-D) - \alpha y(n-D) $$

This gives $|H(\omega)| = 1$ for all $\omega$.

Another interesting effect is a ``chorus'' effect, which would be generated by
several instruments playing the same notes at about the same times, but with
small changes in amplitude and timing.  A simple chorus effect can be
generated with the equation:

$$y(n) = x(n) + \alpha_1 y(n-D_1) + \alpha_2 y(n-D_2) + \alpha_3
y(n-D_3)$$

where $\alpha_i$ and $D_i$ are different.  (For a true chorus effect, these
would change slightly with time.)  To keep the system from saturating, all the
$\alpha$'s must be less than 1/3.

\begin{enumerate}
\item
You should know enough about the 56002 to implement an echo generator.
The 56002 boards in the DSP lab are set up to have 16 kB of memory in the
X data bank.  At a 48~kHz sampling frequency, this will allow delays
of 340 ms.  To allow for longer delays, you can set up the 56002 to sample
at 16~kHz.  This will allow delays of up to one second, which will
make a nice echo, and have a Nyquist frequency of 8~kHz.  Use the 56002
to implement the above difference Equation 1, and try out your echo
generator on an audio signal, using several different values for $\alpha$ and
$D$.

\item Implement a simple reverb.  Use a sampling frequency of
48~kHz, and use a delay of about 1~ms.

\item Implement a simple chorus effect.  

\end{enumerate}

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