[EE - Signals] Question about Discrete-Time Impulse/Discrete-Time Delta

In summary, the conversation discusses the location of a point for a discrete unit impulse at different values of n and whether it is shifted to the left by one unit. The conclusion is that the point would be at location 0 for all values of n, and it would be represented as a stem plot with a vertical line segment at n=-1 and a dot at y=1.
  • #1
user101
207
0
Quick question about a discrete unit impulse.

If I were to draw delta[n+1], at

... etc
n = -2 ... the point would be at location: 0
n = -1 ... the point would be at location: 1
n = 0 ... the point would be at location: 0
n = 1 ... the point would be at location: 0
n = 2 ... the point would be at location: 0
... etc

What I'm asking is that the line that I have in red... is that correct, with the shift of +1 to the left (an advance signal)?

The reason I'm saying it's -1 is because when n is -1, delta[-1+1] is delta[0] = 1.
 
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  • #2
Yes that's right... just like ordinary continuous function... f(x+a) is f(x) shifted a units to the left.
 
  • #3
learningphysics said:
Yes that's right... just like ordinary continuous function... f(x+a) is f(x) shifted a units to the left.

Thanks for the reply. Just to make sure, I would have a "1" dot for y where x = -1 then, correct?
 
  • #4
user101 said:
Thanks for the reply. Just to make sure, I would have a "1" dot for y where x = -1 then, correct?

Yes, that would be correct but usually discrete time signals are as stem plots... ie a vertical line is drawn from the x-axis up to the dot (nothing is drawn when y=0)... eg:

http://en.wikibooks.org/wiki/Digital_Signal_Processing/Discrete_Data#Stem_Plots

So your plot would have a vertical line segment at n=-1 from the x-axis up to the dot at y=1.
 
  • #5
Ok, great! Thanks
 

1. What is the difference between a discrete-time impulse and a discrete-time delta?

A discrete-time impulse is a signal that has a value of 1 at a specific time index and 0 at all other time indices. It is often represented as a vertical line at the specific time index. A discrete-time delta, on the other hand, is a signal that has a value of 1 at all time indices. It is often represented as a horizontal line at the value of 1. In other words, a discrete-time impulse has a single non-zero value, while a discrete-time delta has multiple non-zero values.

2. How are discrete-time impulses and discrete-time deltas used in signal processing?

Discrete-time impulses and discrete-time deltas are often used as test signals in signal processing. They are used to evaluate the behavior of systems and to measure the response of a system to a specific input. They are also used in the analysis and design of filters and other signal processing techniques.

3. Can a discrete-time impulse or delta be applied to a continuous-time system?

Yes, a discrete-time impulse or delta can be applied to a continuous-time system by converting the signal to a continuous-time signal. This can be done by using an impulse train or a Dirac delta function, which are continuous-time equivalents of the discrete-time impulse and delta, respectively.

4. How do you represent a discrete-time impulse or delta in a computer program?

In a computer program, a discrete-time impulse can be represented as an array or vector with a value of 1 at the specific time index and 0 at all other time indices. A discrete-time delta can be represented as a constant array or vector with a value of 1 at all time indices. These representations can vary depending on the programming language and the specific application.

5. What are some real-world examples of discrete-time impulses and deltas?

Discrete-time impulses and deltas are commonly used in digital signal processing applications such as audio and image processing. For example, a discrete-time impulse can be used to test the frequency response of a speaker or microphone, while a discrete-time delta can be used to test the sharpness of an image or the response time of a display. They are also used in communication systems to evaluate the performance of filters and equalizers.

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