# 1.1 Discrete time signals

 Page 1 / 1
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!

## Sequences

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.

## Manipulating sequences

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].

b)Multiplication by a constant c=2. [w(n)]= 2 *[x(n)]= [1.0 4.8 6.4 9.0]

## 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

$(n)=\begin{cases}1 & \text{if n=0}\\ 0 & \text{otherwise}\end{cases}$
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)
$x(n)=\sum_{k=()}$ 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.

$u(n)=\begin{cases}1 & \text{if n\ge 0}\\ 0 & \text{otherwise}\end{cases}$

## Trigonometric functions

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.

$x(n)=\sin (n)$
$x(n)=\cos (n)$

## 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 $i=\sqrt{-1}$ is the imaginary unit.

$x(n)=e^{in}$

## Euler's relations

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

$x(n)=e^{in}=\cos (n)+i\sin (n)$
By complex conjugating and add / subtract the result with we obtain Euler's relations.
$\cos (n)=\frac{e^{in}+e^{-(in)}}{2}$
$\sin (n)=\frac{e^{in}-e^{-(in)}}{2i}$
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
?

Complementary angles
Commplementary angles
Complementary angles
Idrissa
hello
Sherica
im all ears I need to learn
Sherica
Complementary angles
Idrissa
yes
Sherica
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
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.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Got questions? Join the online conversation and get instant answers!