- #1
maysam1
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Suppose that there is a linear relation between discrete time (n) and frequency (f), then what is the relatian between x(n) and X(f) (X(f) is DFT transform of x(n))?
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In summary: Yes, originally there is no relation between time and frequency, but in a system we can assume that f=kn and k is a constant. This means that in this system we can see a linear relation between time and frequency.
- #2
I like Serena
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maysam said:
Hi maysam! Welcome to MHB! (Smile)
I guess we'll need to find the DFT transform of $x(n)=c\cdot n$ where $c$ is some constant.
Can you calculate it?
What is the formula for a DFT?
- #3
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I like Serena
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maysam said:
Hmm... can you clarify what a "linear relation between discrete time (n) and frequency (f)" means?
Presumably we have a signal amplitude $x(n) = x(t_n)$ that depends on time, which transforms to a signal amplitude $X(f) = X(f_k)$ that depends on frequency.
There is no relation between time and frequency.
- #5
maysam1
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I like Serena said:
Yes, originally There is no relation between time and frequency but In a system we can assume that f=kn and k is a constant. this means that in this system we can see a linear relation between time and frequency.
Related to A question about FFT transform
1. What is the FFT transform?
The FFT (Fast Fourier Transform) is a mathematical algorithm used to efficiently convert a discrete signal from its original domain (often time or space) to a representation in the frequency domain and back. It is commonly used in signal processing, image processing, and data compression.
2. How does the FFT transform work?
The FFT algorithm works by taking a signal and breaking it down into smaller signals, called sub-signals, which are then transformed using a mathematical equation. These sub-signals are then combined to reconstruct the original signal in the frequency domain. This process is repeated until the desired level of accuracy is achieved.
3. What are the applications of the FFT transform?
The FFT transform has a wide range of applications, including signal processing (such as filtering and spectral analysis), image processing (such as image compression and enhancement), audio processing, and data compression. It is also used in scientific computing, digital communication systems, and many other fields.
4. What are the advantages of using the FFT transform?
The FFT transform is a highly efficient algorithm, making it significantly faster than other methods for converting signals between the time and frequency domains. It also allows for more accurate and precise analysis of signals, making it a valuable tool in various scientific and engineering applications.
5. Are there any limitations to the FFT transform?
While the FFT transform is a powerful algorithm, it does have some limitations. For example, it assumes that the signal being analyzed is periodic and has a finite length. It also has difficulty with signals that contain sharp peaks or discontinuities. In these cases, alternative methods may be more appropriate.
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