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The signals and relations presented in this module are quite similar to those in the Analog signals module. So do compare and find similarities and differences!
Generally a time discrete signal is a sequence of real or complex numbers. Each component in the sequence is identifiedby an index: ...x(n-1),x(n), x(n+1),...
[x(n)] = [0.5 2.4 3.2 4.5]is a sequence. Using the index to identify a component we have $x(0)=0.5$ , $x(1)=2.4$ and so on.
Given the sequences [x(n)] = [0.5 2.4 3.2 4.5]and [y(n)]= [0.0 2.2 7.2 5.5].
a)Addition. [z(n)]=[x(n)]+[y(n)]=[0.5 4.6 10.4 10.0]
b)Multiplication by a constant c=2. [w(n)]= 2 *[x(n)]= [1.0 4.8 6.4 9.0]
The unit sample is a signal which is zero everywhere except when its argument is zero, thenit is equal to 1. Mathematically
The unit step function is equal to zero when its index is negative and equal to one for non-negative indexes,see for plots.
The discrete trigonometric functions are defined as follows. $n$ is the sequence index and $$ is the angular frequency. $=2\pi f$ , where f is the digital frequency.
The complex exponential function is central to signal processing and some call it the most important signal. Remember that it is a sequence and that $i=\sqrt{-1}$ is the imaginary unit.
The complex exponential function can be written as a sum of its real and imaginary part.
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