What is the Correct Z-Transform of x(n) = -2^n u(-n-1)?

In summary, the Z-transform is a mathematical representation of a discrete-time signal in the frequency domain using a complex variable, z. It is a generalization of the Fourier transform for discrete-time signals and is commonly used in digital signal processing applications and control systems for analyzing and manipulating signals. The inverse Z-transform is the process of converting a Z-transformed signal back to its original form in the time domain.
  • #1
nelectrode
10
0
Hi guys,

I am trying to find the z-tranform of the following equation: x(n) =-2n u(-n-1)

Using the Z-transform definition,summation and geometric series
I am getting 1/(1-2z-1)

But according to my lecturer the answer is suppose to be 0.5/(1-2z-1)

I have tried simplification/factorization and still seems to be wrong.

Thanks
 

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  • #2
What does u mean?
Can you show your steps?
 

1. What is the Z-transform of a sequence?

The Z-transform of a sequence is a mathematical representation that relates a discrete-time signal to a complex variable, z. It is used to analyze and manipulate discrete-time signals in the frequency domain.

2. How is the Z-transform different from the Fourier transform?

The Z-transform is a generalization of the Fourier transform for discrete-time signals. While the Fourier transform is used for continuous-time signals, the Z-transform is used for discrete-time signals. Additionally, the Z-transform takes into account both the magnitude and phase of the signal, while the Fourier transform only considers the magnitude.

3. What is the purpose of using the Z-transform?

The Z-transform allows for the analysis and manipulation of discrete-time signals in the frequency domain. It is commonly used in digital signal processing applications such as filtering and system analysis.

4. How is the Z-transform used in control systems?

The Z-transform is used in control systems to analyze the stability and performance of a system in the frequency domain. It allows for the design of controllers and filters to achieve desired system responses.

5. What is the inverse Z-transform?

The inverse Z-transform is the process of converting a Z-transformed signal back to its original discrete-time form. It is used to obtain the time-domain representation of a signal after analyzing it in the frequency domain using the Z-transform.

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