Understanding Time Invariance in Signals

In summary, the conversation discusses the concept of time invariance in signals. The key technique to determine time invariance is to look at the parameters beside the function and see if they contain a t term or are constants. The example of x[-n] is used to demonstrate this concept, and it is concluded that the signal is not time invariant due to the presence of n in the function. The conversation also mentions a test for time invariance using the delay and system effects on the signal. Ultimately, the conversation ends with a discussion on the importance of understanding the test for time invariance.
  • #1
kolycholy
39
0
i usually have such a hard time determining whether a signal is time invariant or not ...

for example, why would x[-n] not be time-invariant?

please don't just tell me why x[-n] would not be time invariant ...
tell me techniques that I can apply to other signals too
 
Engineering news on Phys.org
  • #2
look at the parameters beside your function if they contain a t term then your signal is time varient while if the parameters are constants then the signal is time invarient.
 
  • #3
angel23 said:
look at the parameters beside your function if they contain a t term then your signal is time varient while if the parameters are constants then the signal is time invarient.
that makes sense ... but then tell me why x[-n] is not time invariant?
 
  • #4
do you see any t terms beside the function??
it is time invarient. why r u sure it isn't time invarient?
you can use this site to see the graph for check. http://www.jhu.edu/~signals/sys/resulta939.html

(i used unit step as an example)
 
Last edited by a moderator:
  • #5
angel23 said:
do you see any t terms beside the function??
it is time invarient. why r u sure it isn't time invarient?
you can use this site to see the graph for check. http://www.jhu.edu/~signals/sys/resulta939.html

(i used unit step as an example)
i am so sure it isn't time invariant, because the solution manual said so ...
 
Last edited by a moderator:
  • #6
What is 'n'?
 
  • #7
desA said:
What is 'n'?
n is just time, but it assumes discrete value only
 
  • #8
So, you've answered your own question.
 
  • #9
desA said:
So, you've answered your own question.
no i did not ... please enlighten me ...
 
  • #10
i am sure it is time invarient my mind says so.
 
  • #11
The key is in understanding the test for time invariance.

To test: x[n] > DELAY > x[n-n0] > SYSTEM > w[n]
|
>>> SYSTEM > y[n] > DELAY > y[n-n0]

w[n] and y[n-n0] are equal if the system is time invariant

in the case of y[n]=x[-n], for the top approach, delaying the system results in n-n0 then we apply the system's effect of reversing JUST n, so w[n]=x[-n-n0]. With the second path, we apply the system and get y[n]=x[-n] and then apply the delay to get y[n-n0]=x[-(n-n0)]=x[-n+n0].

Since x[-n-n0] is not the same as x[-n+n0] the system is time VARIANT.
 

1. What is time invariance in signals?

Time invariance in signals refers to the property of a system or signal where changes in the input or independent variable do not affect the output in terms of time shift. In other words, the output of a time-invariant system or signal remains the same regardless of when the input is applied.

2. Why is time invariance important in signal processing?

Time invariance is important in signal processing because it allows for the analysis and manipulation of signals without having to consider the time at which the signal is being observed. This simplifies the process and allows for easier comparison and combination of different signals.

3. How can time invariance be tested in a system or signal?

Time invariance can be tested by applying a time-shifted input to the system or signal and comparing the resulting output with the original output. If the output remains the same, the system or signal is considered time-invariant.

4. What are some examples of time-invariant signals?

Some examples of time-invariant signals include sinusoidal waves, exponential decay or growth signals, and any periodic signal. These signals have consistent patterns and characteristics regardless of when they are observed.

5. How does time invariance relate to other properties of signals?

Time invariance is closely related to other properties of signals such as linearity and causality. A time-invariant signal is also linear, meaning that scaling or adding inputs will result in a corresponding scaling or addition of outputs. However, time invariance does not necessarily imply causality, as a non-causal signal can still be time-invariant.

Similar threads

Is my understanding of the Nyquist theorem correct?
    • Electrical Engineering
Replies
4
Views
796
I Time dilation vs Differential aging vs Redshift
    • Special and General Relativity
Replies
21
Views
474
Can I run cable tv signal and on air tv signal in a single coax?
    • Electrical Engineering
Replies
9
Views
2K
Discrete-time Signal & Periodicity condition
    • Electrical Engineering
Replies
1
Views
1K
I What, exactly, are invariants?
    • Special and General Relativity
5
Replies
144
Views
6K
Understand the concept of bandwidth
    • Electrical Engineering
Replies
24
Views
2K
I General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
    • Linear and Abstract Algebra
Replies
1
Views
144
Lomb-Scargle periodogram for complex exponential signal
    • Electrical Engineering
Replies
0
Views
314
How to synchronize the RF source having delay over time?
    • Electrical Engineering
Replies
8
Views
717
How can I convert audio signals into pulses for radio transmission?
    • Electrical Engineering
Replies
20
Views
1K

Hot Threads

Recent Insights

Back
Top