Digital Signal Processing Reference
In-Depth Information
for i=1:length(X)
if (real(X(i)) > 0)
phase(i) = atan(imag(X(i)) / real(X(i)));
elseif (real(X(i)) < 0)
% Add to +/- pi, depending on quadrant of the point
if (imag(X(i)) < 0) % then we are in quadrant 3
phase(i) = -pi + atan(imag(X(i)) / real(X(i)));
else
% we are in quadrant 2
phase(i) = pi + atan(imag(X(i)) / real(X(i)));
end
else
% If real part is 0, then it lies on the + or - y-axis
% depending on the sign of the imaginary part
phase(i) = sign(imag(X(i)))*pi/2;
end
end
1.2
What Is a Signal?
A signal is a varying phenomenon that can be measured. It is often a physical
quantity that varies with time, though it could vary with another parameter, such
as space. Examples include sound (or more precisely, acoustical pressure), a voltage
(such as the voltage dierences produced by a microphone), radar, and images trans-
mitted by a video camera. Temperature is another example of a signal. Measured
every hour, the temperature will uctuate, typically going from a cold value (in the
early morning) to a warmer one (late morning), to an even warmer one (afternoon),
to a cooler one (evening) and nally a cold value again at night. Often, we must
examine the signal over a period of time. For example, if you are planning to travel
to a distant city, the city's average temperature may give you a rough idea of what
clothes to pack. But if you look at how the temperature changes over a day, it will
let you know whether or not you need to bring a jacket.
Signals may include error due to limitations of the measuring device, or due to
the environment. For example, a temperature sensor may be aected by wind chill.
At best, signals represented by a computer are good approximations of the original
physical processes.
Some real signals can be measured continuously, such as the temperature. No
matter what time you look at a thermometer, it will give a reading, even if the
time between the readings is arbitrarily small. We can record the temperature at
intervals of every second, every minute, every hour, etc. Once we have recorded these
