Signals Systems System Response
Frequency Representation Fourier Series / Transforms Background Material

Most functions are given to us in the time domain. We are most familiar with trigonometric functions like:

y(t) = sin(t) or y(t) = cos(t), which can be generalized to y(t) = sin(2πft) or y(t) = cos(2πft) where

ω = 2πf.

(ω - omega - is the angular frequency with units [rad/s] and f - frequency - is the frequency with units of Hz [1/s])

Sometimes it is useful to be able to represent a function by its frequency content. A graph of the frequency domain plots frequency against the amplitude of a particular frequency (where 0 Hz or radians is DC - direct current).

Power Spectral Density

The power spectral density is an example of a graph of amplitude versus frequency. It is used to see the strength of each frequency for a particular system. Mathematically, it is the Fourier transform of the autocorrelation function.

Figure 2. PSD of systolic blood pressure and RR-interval in a young healthy subject.

(from http://www.cbi.dongnocchi.it/glossary/PowerSpectralDensity.html)

Fourier Series

Every periodic signal can be represented by a series of sines and cosines. As we increase the number of terms in the series, the signal will be approximated more and more accurately. Let's see how this works. Take a sawtooth, for example,

0-terms
1-term
2-terms
3-terms
4-terms
5-terms
7-terms
10-terms
20-terms
50-terms
100-terms

For more information, refer to the following websites:

is website was sponsored by the Johns Hopkins Technology Fellowship Program and developed Bennett Landman, Issel Anne Lim, Alan Huang, William Feng, and Pavan Patel under the guidance of Dr. Michael Miller. © Copyright 2008. Johns Hopkins University. All rights reserved.

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