**Speech Processing
by Computer**

LAB 2

DIGITAL
SYSTEMS

This lab session
demonstrates some simple linear systems operating upon a digital signal. A program allows the input of the operating
coefficients of a small linear system, displays the frequency response and
replays a signal before and after processing.

1. Amplification
and Attenuation

(i) Acquire a speech signal at 20000
samples/second.

(ii) Use the 'ltitest' program to scale the
input samples x[n] by 2.0 to increase the amplitude by 6dB. That is, set y[n] = 2 * x[n].

(iii) Use the 'ltitest' program to scale the
input samples x[n] by 0.5 to decrease the amplitude by 6dB. That is, set y[n] = 0.5 * x[n].

2. Non-recursive
low-pass filtering

(i) Acquire a speech signal at 20000
samples/second.

(ii) Use the 'ltitest' program to output the
average of the current sample x[n] with previous sample x[n-1]. That is y[n] = 0.5 * x[n] + 0.5 *
x[n-1]. At what frequency is the zero?

(iii) Use the 'ltitest' program to output the
average of the current sample x[n] with previous two samples x[n-1] and
x[n-2]. That is y[n] = 0.33 * x[n] +
0.33 * x[n-1] + 0.33 * x[n-2]. At what
frequency is the zero?

(iv) Use the 'ltitest' program to output the
average of the current sample x[n] with previous three samples x[n-1], x[n-2]
and x[n-3]. That is y[n] = 0.25 * x[n]
+ 0.25 * x[n-1] + 0.25 * x[n-2] + 0.25 * x[n-3]. At what frequencies are the zeros?

3. Non-recursive
high-pass filter

(i) Acquire a speech signal at 20000 samples/second.

(ii) Use the 'ltitest' program to output the
difference between the current sample x[n] and previous sample x[n-1]. That is y[n] = x[n] - x[n-1]. At what frequency is the zero?

4. Recursive implementation of a simple
resonator

The
formulae for a simple resonator are as follows:

Take f = resonator
frequency as fraction of sample rate

Take b = resonator
bandwidth as fraction of sample rate

Then parameter r =
(1-b/2)

and coefficient of
y[n-1] = 2 * r * cos(2*π*f)

and coefficient of
y[n-2] = - r * r

(i) Acquire a speech signal at 20000
samples/second.

(ii) Use the 'ltitest' program to pass the
signal through a simple resonator at a natural frequency of 2000Hz and a
bandwidth of 500Hz.

(iii) Use the 'ltitest' program to pass the
signal through a simple resonator at a natural frequency of 1000Hz and a
bandwidth of 100Hz. You may need to
scale the input to stop overloading, how might you do this?