Time Shifting & Stretching: Questions Explained

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In summary, the first example of time shifting and stretching suggests that if y(t) is equal to x(3t), then x(t) is equal to y(t/3). However, in the second example, where y(t) is equal to (-1/2)x(-3t+2), the relationship between x(t) and y(t) is not as straightforward. Instead, the use of a variable u is necessary to properly represent the relationship between the two functions.
  • #1
lennybogzy
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I have a question regarding time shifting, stretching etc. For example:

if I have y(t) = x(3t) does that mean that x(t) = y(t/3)?

if I have y(t)=(-1/2)x(-3t+2) does x(t) = -2y(t/3 -2) ?
 
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  • #2
lennybogzy said:
I have a question regarding time shifting, stretching etc. For example:

if I have y(t) = x(3t) does that mean that x(t) = y(t/3)?

Yes.

if I have y(t)=(-1/2)x(-3t+2) does x(t) = -2y(t/3 -2) ?

No. Let u = -3t+2 so t = (-1/3)(u-2). This gives

y((-1/3)(u-2))=(-1/2)x(u)

-2y((-1/3)(u-2)) = x(u). Replace the u by t and it's a little different than what you wrote.
 
  • #3
brilliant! thanks
 

Related to Time Shifting & Stretching: Questions Explained

1. What is time shifting and stretching?

Time shifting and stretching is the process of altering the duration or speed of a recording without changing the pitch. It allows for the compression or expansion of time, making a recording shorter or longer while maintaining the original pitch and tempo.

2. How is time shifting and stretching used in scientific research?

In scientific research, time shifting and stretching is commonly used in the analysis of audio and video data. It allows for the precise synchronization and alignment of different recordings, making it easier to compare and analyze data from multiple sources.

3. What are the potential benefits of time shifting and stretching?

One of the main benefits of time shifting and stretching is the ability to manipulate and analyze data in a more precise and efficient manner. It also allows for the creation of new and unique sounds and visuals, making it a useful tool in the fields of music and film production.

4. Are there any limitations to time shifting and stretching?

While time shifting and stretching can be a powerful tool, it also has its limitations. It is not always possible to alter the duration or speed of a recording without affecting the quality or integrity of the data. Additionally, extreme time stretching can result in a loss of clarity and distortion of the original recording.

5. Is time shifting and stretching ethical?

Time shifting and stretching itself is a neutral process and can be used for both ethical and unethical purposes. However, the ethical considerations arise when the altered recordings are used for commercial purposes or without the consent of the original creators. It is important to respect copyright laws and obtain permission before manipulating someone else's work.

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