Digital Signal Processing Reference
In-Depth Information
This sequence of values, the samples of the sine wave, can be used to completely reconstruct the
original continuous domain sine wave using a DAC. There are, of course, a number of conditions to
ensure that this is possible, and they are taken up in detail in the next chapter.
To compute and plot the sample values of a 2-Hz sine wave sampled every 0
.
05 second on the
time interval 0 to 1
.
1 second, make the following MathScript call:
t = [0:0.05:1.1]; figure; stem(t,sin(2*pi*2*t))
where the
t
vector contains every sample time
nT
with
T
= 0.05. Alternatively, we might write
T = 0.05; n = 0:1:22; figure; stem(n*T,sin(2*pi*2*n*T))
both of which result in Fig. 2.2.
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
0
0.2
0.4
0.6
0.8
1
Time, seconds
Figure 2.2:
A plot of the samples of a sine wave having frequency 2 Hz, sampled every 0.05 second up
to time 1.1 second.
2.4 USEFUL SIGNALS, SEQUENCES, AND CONCEPTS
2.4.1 SINE AND COSINE
We saw above that a sine wave of frequency
f
periodically sampled at the time period
T
has the values
s
[
n
]=
sin
[
2
πf nT
]
