This expression shows that the instantaneous frequency goes from f 0 f
n 0 to f N À 1 f
at time n N À 1.
Because of the complexity of the linear chirp signal generator, it is more convenient
for real-time applications to generate such a sequence by a general-purpose computer
and store it in a lookup table. Then the lookup-table method introduced in Section 9.1.1
can be used to generate the desired signal.
An interesting application of chirp signal generator is generating sirens. The elec-
tronic sirens are often created by a small generator system inside the vehicle compartment.
This generator drives either a 60 or 100 Watt loudspeaker system present in the light bar
mounted on the vehicle roof or alternatively inside the vehicle radiator grill. The actual
siren characteristics (bandwidth and duration) vary slightly from manufacturers. The
wail type of siren sweeps between 800 Hz and 1700 Hz with a sweep period of approxi-
mately 4.92 seconds. The yelp siren has similar characteristics to the wail but with a
period of 0.32 seconds.
9.1.3 DTMF Tone Generator
A common application of sinewave generator is the all-digital touch-tone phone that
uses a dual-tone multi-frequency (DTMF) transmitter and receiver. DTMF also finds
widespread use in electronic mail systems and automated telephone servicing systems in
which the user can select options from a menu by sending DTMF signals from a
Each key-press on the telephone keypad generates the sum of two tones expressed as
where T is the sampling period and the two frequencies f
uniquely define the
key that was pressed. Figure 9.1 shows the matrix of sinewave frequencies used to
encode the 16 DTMF symbols. The values of the eight frequencies have been chosen
carefully so that they do not interfere with speech.
The low-frequency group (697, 770, 852, and 941 Hz) selects the four rows frequencies
of the 4 Â 4 keypad, and the high-frequency group (1209, 1336, 1477, and 1633 Hz)
1477 1633 Hz
Figure 9.1 Matrix telephone keypad
SINEWAVE GENERATORS AND APPLICATIONS