Time Scaling of Signals

[anuragmash]

I have a very basic question to ask! I have just started a course on signals and systems and I am finding time shifting and time scaling very confusing. I don't understand how by multiplying by a factor >1 the original signal gets compressed i.e. why is x(4t) is a compressed version of x(t). Please can any1 help regarding this. Can any1 give me a sound explanation regarding this question! Thanks in advance...

 

[ahmad1954]

let explain the problem with your example: x(t)=t so x(4t)=4t. if we want calculate two function in 1, x(1)=1 but in second function we should use t=1/4 because we want 1 in parentheses and if you draw these functions you can see second function is compress.

 

[Logendran]

Refer the below link for the clear concept on your doubt. I hope it would be more helpful and easy to understand

https://cnx.org/content/m10125/latest/

 

[anuragmash]

Thanks for your answer ahmad1954!!!
I didn't quite understand what you meant by "if we want calculate two function in 1"...what i did understand is that in the transformed graph the time axis is 1/a times (say t') the original graph's time axis (say t)...but how does the transformed graph become x(2t') i cannot understand. Can you please elaborate a bit. Thanks in advance...!!!!

 

[ahmad1954]

x(t)=t and x(4t)=4t. suppose y(t)=x(4t)=4t. so x(t)=t and y(t)=4t. now if draw these function you can see scaling on y(t). do you understand?

 

[gn.times]

If t becomes 2t means actually the FREQUENCY is multiplied twice not the time.
Hence time period automatically contracts. Hope you got it.