Digital Signal Processing Reference
In-Depth Information
j sin() =
e
j
2
j
e
:
2
This means that a complex signal has two frequency components as well. Of course,
if we had a signal such as cos() + j sin(), we would have:
cos() + j sin() =
e
j
2
j
+
e
j
2
j
+
e
e
:
2
2
If equals , then
cos() + j sin() = e
j
:
For this reason, we concern ourselves with only the rst half of the frequency
response. When it looks like Figure 6.14, we say it is a lowpass lter. This means
that any low-frequency (slowly changing) components will remain after the signal
is operated on by the system. High-frequency components will be attenuated, or
\ltered out." When it looks like Figure 6.15, we say it is a highpass lter. This
means that any high-frequency (quickly changing) components will remain after the
signal is operated on by the system.
1
f
s
2
Figure 6.14: Frequency response of a lowpass lter.
The frequency response can be found by performing the DFT on a system's
output when the impulse function is given as the input. This is also called the
\impulse response" of the system. To get a smoother view of the frequency response,
the impulse function can be padded with zeros.
1
f
2
Figure 6.15: Frequency response of a highpass lter.
The more samples that are in the input function to the DFT, the better the
resolution of the output will be.
