Page 64 - Prosig Catalogue 2005

SOFTWARE PRODUCTS
THE BASICS OF DIGITAL FILTERING

Finally the “Impulse Response” function was formed by calculating an
inverse FFT of the “transfer function” and selecting the timeshift option to
get positive and negative time shown.
Training & Support

Figure 2: A Swept Sinewave
We can seen the simple sine wave is a repeating pattern, but the swept
Condition Monitoring delay as -11 msec as expected. but the swept sine wave has a varying frequency, starting at 1Hz and
sine wave is increasing in frequency. That is, the time between the peaks
is reducing. The simple sine wave has a fundamental frequency of 1Hz,
The peak is just before zero. Showing an expanded view reveals the time
finishing at 10Hz over the 2 seconds time period.
Figures 3 and 4 show the simple sinewave and swept sinewave in the
frequency domain. As we can see the sinewave has one dominant
frequency spike, whilst the swept sinewave shows a spread of frequencies
representing the range of the sweep from 1Hz to 10Hz.

Software If we had just inverse transformed the cross spectrum we would have

just got the correlation function. Dividing by the input auto spectrum
is useful however because it effectively normalizes the data. Another
helpful scheme is to multiply the cross spectrum by the coherence as this
effectively eliminates the unrelated parts. This is not necessary here as Figure 3: Spectrum of simple sinewave
we have a sufficient signal to noise ratio.
The Basics Of Digital

Hardware Filtering

Recently when discussing with an engineering student the characteristics
of filters, it became clear that some confusion exists around this subject
area. Here we will attempt to explain the differences between low pass,
high pass, band pass & band stop filters.
To begin we will cover some basics of signal processing. This article uses
swept sinewaves to explain filtering, so first we must understand what
they are.
Figure 4: Spectrum of swept sinewave
So the two types of sinewave are quite similar when viewed in the time
System Packages frequency content in the swept sine wave changes uniformly across the
domain. If viewing a single cycle it would be hard to distinguish them.
However their frequency content is very different. Importantly, the
time range of the signal.
The rest of the article will discuss the swept sine wave and the effects of
certain types of filter on this swept sine wave.
Let’s look at the 4 basic types of filter. Low pass, high pass, band pass and
band stop. Each of these filters has different frequency characteristics.

the high frequencies. The cut off frequency is the frequency that the
filter begins to attenuate the content. So a low pass filter set at 100Hz
Figure 1: A Simple Sinewave Low pass filters will allow the low frequencies to pass through, but block
64 http://prosig.com +1 248 443 2470 (USA) or contact your
+44 (0)1329 239925 (UK) local representative
sales@prosig.com
A CMG Company