Solving for the DTFT of (0.8)^n u[n]

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In summary, the problem is asking to compute the DTFT of the signal x[n] = (0.8)^n u[n]. The solution involves using the properties of DTFT, and the answer can be found on page 20 of the provided DTFT table. Alternatively, the professor may want the student to derive the answer using the properties discussed in the course material.
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Homework Statement


Compute the DTFT of the following signal.

[tex]x[n] = (0.8)^n u[n][/tex]


Homework Equations


Properties of DTFT


The Attempt at a Solution


Well, my professor tells me to use the properties of DTFT to solve this. I'd love to - except I don't know what the DTFT of [tex](0.8)^n[/tex] is. I've tried looking it up on the DTFT table, but couldn't find any, can someone tell me what it is?
 
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It's in the DTFT pairs here:

http://www.neng.usu.edu/classes/ece/5630/notes_transforms.pdf [Broken] on page 20.

but maybe the prof wants you to derive it from the properties you already have in your text?
 
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1. What is the DTFT of (0.8)^n u[n]?

The DTFT (Discrete-Time Fourier Transform) of (0.8)^n u[n] is a mathematical representation of the frequency components of the discrete-time signal (0.8)^n u[n]. It is a complex-valued function that describes how much of each frequency component is present in the signal.

2. How do you solve for the DTFT of (0.8)^n u[n]?

To solve for the DTFT of (0.8)^n u[n], you can use the definition of the DTFT which involves summing the signal over all time values and multiplying by a complex exponential function. In this case, the complex exponential function will be (0.8)^n e^(-jwn), where w is the frequency.

3. What are the properties of the DTFT of (0.8)^n u[n]?

The DTFT of (0.8)^n u[n] has several properties, including linearity, time shifting, frequency shifting, time reversal, and convolution. These properties can be used to simplify the calculation of the DTFT and to understand the frequency components of the signal.

4. What is the significance of the DTFT of (0.8)^n u[n]?

The DTFT of (0.8)^n u[n] is significant because it allows us to analyze the frequency components of a discrete-time signal. This can be useful in areas such as digital signal processing, communication systems, and control systems.

5. How does the value of (0.8)^n affect the DTFT of u[n]?

The value of (0.8)^n in the signal (0.8)^n u[n] affects the DTFT by scaling the amplitude of the frequency components. The larger the value of (0.8)^n, the smaller the amplitude of the frequency components will be. This can be seen in the magnitude plot of the DTFT, where the amplitude decreases as the frequency increases.

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