# [Week 2] Signals and Systems

Things are getting more exciting!

The week is divided to three segments. The first segment introduced some 2D and 3D discrete signals such as Images and videos, mentioning the meaning of Unit Impulse and Unit Step discrete signals, also the segment shows the separation availability between multiple numbers of signals.

In the second segment. It introduced the 2-dimenational complex exponential signal and how to build blocks of signals that have the same frequencies.

In the third segment. It was about 2D convolution examples in which some filters are used to manipulate the original image to produce an output image.

2D and 3D Discrete Signals

• 2D discrete signals are signals that depend on 2 variables, each one of them has its own minimum and maximum values.
• Example: Images
• 2D Image consists of pixels, each pixel has its x-y coordinate in the image
• The pixel holds 3 combined values which represent the RED, GREEN and BLUE values
• If the image is Gray-scaled, this means that RED == GREEN == BLUE
• 3D discrete signals have an additional variable
• Videos could be considered 3D discrete signals because the dimensions are: x, y, z, where is z is the frame number in the video, and x, y are the dimension of the frame  Discrete Unit Impulse

Discrete Unit Step

Complex Exponential Signals

2D Systems

Linear System

Spatially Invariant Systems

Linear and Spatially Invariant Systems Examples for 2D convolution

• Noise Reduction
• Edge Detection
• Sharpen
• Blur

References