Discrete Time Fourier Transform

In summary, The Discrete Time Fourier Transform (DTFT) is a mathematical concept used to convert a discrete, time-domain signal into a continuous, frequency-domain representation. It is commonly used in signal processing and communications applications. The main difference between the DTFT and DFT is that the DTFT operates on a continuous frequency spectrum, while the DFT operates on a discrete frequency spectrum. The DTFT is calculated by applying a mathematical formula that involves a summation over all possible frequencies. While it can be used for real-world signals, it is more commonly used for analyzing signals with infinite duration.
  • #1
Mr.Tibbs
24
0
Find the DTFT of:

h[n]=(-1)[itex]^{n}[/itex][itex]\frac{sin(\frac{\pi}{2}n}{sin(\pi n}[/itex]

useful properties:

x[n]y[n] --> X[Ω]*Y[Ω]

[itex]\frac{sin(\frac{\pi}{2}n}{sin(\pi n}[/itex] --> rect[[itex]\frac{2Ω}{\pi}[/itex]


I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . .

any help would be appreciated
 
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  • #2
Mr.Tibbs said:
I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . .
Why do you say that?
 

1. What is the Discrete Time Fourier Transform (DTFT)?

The Discrete Time Fourier Transform is a mathematical concept used to convert a discrete, time-domain signal into a continuous, frequency-domain representation. It is used to analyze the frequency components of a signal and is an important tool in signal processing and communications.

2. How is the DTFT different from the Discrete Fourier Transform (DFT)?

The main difference between the DTFT and DFT is that the DTFT operates on a continuous frequency spectrum, while the DFT operates on a discrete frequency spectrum. This means that the DTFT is better suited for analyzing signals with infinite duration, while the DFT is better for analyzing finite-duration signals.

3. What are some applications of the DTFT?

The DTFT is commonly used in signal processing applications such as audio and image processing, telecommunications, and data compression. It is also used in areas such as control systems, digital filters, and spectral analysis.

4. How is the DTFT calculated?

The DTFT is calculated by taking the discrete time signal and applying a mathematical formula that converts it into its frequency domain representation. This formula involves a summation over all possible frequencies and is typically implemented using computer algorithms.

5. Can the DTFT be used for real-world signals?

Yes, the DTFT can be used for real-world signals, but it is typically used for analyzing signals with infinite duration. In practice, signals are often finite in duration, so the DFT is a more commonly used tool. However, the DTFT can still be useful in certain applications, such as analyzing the frequency components of a periodic signal.

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