Biomedical Engineering Reference
In-Depth Information
Forward
Time domain
Frequency domain
T
R
A
N
S
F
O
R
M
Diff. equation
Complex s-plane
D.E.
Operations:
Operations:
Product
Derivative
Integration
Division
Answer: number
results
Inverse
FIGURE 12.1
:
Transformation from the time domain to the frequency domain
one domain, that is, time domain, into a separate domain, that is, frequency domain with
either the La Place or Fourier Basis functions. The reason for working in the transformed
domain is to reduce the time-domain operations of integration or differentiation to less
complex operations of division or multiplication, respectively.
There are numerous forms of the Fourier Transform. The most used forms include
the following:
1.
The Fourier Trigonometric Series, which was used prior to the advent of com-
puter to analyze analog data, but had the major drawback of being very time
consuming.
2.
The Discrete Fourier Transform was used with digitized data, and is considered
to be a subset of the LaPlace Transform; however, the Discrete Fourier Transform
was also very time consuming (4 minutes to analyze 1024 samples of data).
3.
The Fast Fourier Transform became the most popular method used to per-
form transformation into the frequency domain because it was very efficient and
fast.
There are many other Fourier Transforms that will not be studied in this course.
The Fourier analysis consists of two basic operations:
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