<< Chapter < Page Chapter >> Page >
Important discrete time signals

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.

Got questions? Get instant answers now!

Manipulating sequences

  • Addition

    Add individually each component with similar index
  • Multiplication by a constant

    Multiply every component by the constant
  • Multiplication of sequences

    Multiply each component individually
  • Delay

    A delay by k implies that we shift the sequence by k. For this to make sense the sequence has to be of infinite length.

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]

Got questions? Get instant answers now!

Elementary signals&Relations

The unit sample

The unit sample is a signal which is zero everywhere except when its argument is zero, thenit is equal to 1. Mathematically

n 1 n 0 0
The unit sample function is very useful in that it can be seen as the elementary constituent in any discrete signal.Let x n be a sequence. Then we can express x n as follows (using the unit sample definition and the delay operation)
x n k x k n k

The unit step

The unit step function is equal to zero when its index is negative and equal to one for non-negative indexes,see for plots.

u n 1 n 0 0
Unit step function, no delay.
Unit step function, delayed by 5.
Two unit step functions.

Trigonometric functions

The discrete trigonometric functions are defined as follows. n is the sequence index and is the angular frequency. 2 f , where f is the digital frequency.

x n n
x n n
A discrete sine with digital frequency 1/20.

The complex exponential function

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 1 is the imaginary unit.

x n n

Euler's relations

The complex exponential function can be written as a sum of its real and imaginary part.

x n n n n
By complex conjugating and add / subtract the result with we obtain Euler's relations.
n n n 2
n n n 2
The importance of Euler's relations can hardly be stressed enough.

Matlab files


Take a look at

  • Introduction
  • Analog signals
  • Discrete vs Analog signals
  • Frequency definitions and periodicity
  • Energy&Power
  • Exercises

Questions & Answers

a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
f(n)= 2n + 1
Samantha Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Got questions? Join the online conversation and get instant answers!
QuizOver.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Information and signal theory. OpenStax CNX. Aug 03, 2006 Download for free at http://legacy.cnx.org/content/col10211/1.19
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Information and signal theory' conversation and receive update notifications?