Math Problem Statement

nối đáp án

Từ một tín hiệu ban đầu x(t), các thao tác sau đây sẽ tạo ra tín hiệu nào trong các tín hiệu sau đây?

Solution

The image you uploaded contains a signal processing question in Vietnamese. The question involves various transformations of a signal x(t)x(t), including scaling, shifting, and time reversal, and asks which of the options provided matches a series of operations on the signal.

The operations include:

  1. Scaling the signal by a factor KK.
  2. Shifting the signal by aa seconds forward and backward.
  3. Time reversal (flipping the signal around the t=0t=0 axis).
  4. Various combinations of these transformations.

The problem asks you to identify the result after applying a series of these transformations to the initial signal x(t)x(t).

Steps to solve:

You need to apply the transformations step by step. For example:

  • Scaling the signal: x(t)x(Kt)x(t) \rightarrow x(Kt) or x(t/K)x(t/K)
  • Shifting the signal: x(t)x(ta)x(t) \rightarrow x(t - a)
  • Time reversal: x(t)x(t)x(t) \rightarrow x(-t)

After applying these operations, you will match the result with the options listed as (a), (b), (c), etc.

Would you like me to solve a specific part of this question, or guide you through the solution in more detail?

Relative Questions:

  1. What is the general effect of scaling a signal by a factor KK?
  2. How does time-shifting by aa seconds affect the signal mathematically?
  3. Can you explain the result of time reversal on a signal?
  4. How do multiple transformations (scaling, shifting, reversing) combine in a single expression?
  5. What are common mistakes when combining signal transformations?

Tip:

Always apply the transformations in the correct order as specified in the problem, since the order of operations matters in signal processing.

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Math Problem Analysis

Mathematical Concepts

Signal Processing
Time Scaling
Time Shifting
Time Reversal

Formulas

Scaling: x(t) → x(Kt) or x(t/K)
Shifting: x(t) → x(t - a)
Time Reversal: x(t) → x(-t)

Theorems

Time Scaling Theorem
Time Shifting Theorem
Time Reversal Theorem

Suitable Grade Level

Undergraduate Level (Electrical Engineering or Signal Processing)