Signals are sometimes classified by their symmetry along the time axis relative to the origin, t = 0. Even signals fold about t = 0, and odd signals fold about t = 0 but with a sign change. Simply put,
![image0.jpg](https://www.dummies.com/wp-content/uploads/405371.image0.jpg)
To check the even and odd signal classification, use the Python rect() and tri() pulse functions to generate six aperiodic signals. Here’s the code for generating two of the signals:
In [<b>759</b>]: t = arange(-5,5,.005) # time axis for plots In [<b>760</b>]: x1 = ssd.rect(t+2.5,3)+ssd.rect(t-2.5,3) In [<b>763</b>]: x4 = ssd.rect(t+3,2)-ssd.tri(t,1) +ssd.rect(t-3,2)
Check out the six signals, including the classification:
![image1.jpg](https://www.dummies.com/wp-content/uploads/405372.image1.jpg)
To discern even or odd, observe the waveform symmetry with respect to t = 0. Signals x1(t), x4(t), and x6(t) are even; they fold nicely about t = 0. Signals x2(t) and x5(t) fold about t = 0 but with odd symmetry because the waveform on the negative time axis has the opposite sign of the positive time axis signal.
Signal x3(t) is neither even nor odd because a portion of the waveform, the triangle, is even about 0, while the rectangles are odd about 0. Taken in combination, the signals are neither even nor odd.
A single sinusoid in cosine form, without any phase shift, is even, because it’s symmetric with respect to t = 0, or rather it’s a mirror image of itself about t = 0. Mathematically, this is shown by the property of being an even signal:
![image2.jpg](https://www.dummies.com/wp-content/uploads/405373.image2.jpg)
Similarly, a single sinusoid in sine form, without any phase shift, is odd, because it has negative symmetry about t = 0. Instead of an exact mirror image of itself, values to the left of t = 0 are opposite in sign of the values to the right of t = 0. This is mathematically an odd signal:
![image3.jpg](https://www.dummies.com/wp-content/uploads/405374.image3.jpg)
If a nonzero phase shift is included, the even or odd properties are destroyed.