Discrete Fourier Transform Frequency

In summary, the frequency values for the discrete Fourier transform can be computed by using a sine function at a specific frequency and using the formula \frac{n}{N} F_s where n is the index of the sample and F_s is the sampling frequency.
  • #1
Chemistopher
2
0
Hi everybody,

I'm in the process of writing a discrete Fourier transform program using the algorithm on the DFT wikipedia page. When I throw in functions that I know the frequency domain signal of it gives the predicted shape but I have absolutely know idea how to generate a frequency axis.

Does anybody here know how I can compute the frequency values?

Thanks in advance.

Chris
 
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  • #2
Try using a sine function at a specific frequency. Then whatever you get for the Fourier Transform corresponds to that frequency.
 
  • #3
Chemistopher said:
Hi everybody,

I'm in the process of writing a discrete Fourier transform program using the algorithm on the DFT wikipedia page. When I throw in functions that I know the frequency domain signal of it gives the predicted shape but I have absolutely know idea how to generate a frequency axis.

Does anybody here know how I can compute the frequency values?

Thanks in advance.

Chris

The DFT gives you N evenly spaced samples of the DTFT (discrete-time Fourier transform). The frequencies corresponding to these samples are

[tex]\frac{n}{N} F_s[/tex]

where [itex]n = 0,1,\ldots,N-1[/itex] are the indices of the samples, and [itex]F_s[/itex] is the sampling frequency of the input sequence.
 

FAQ: Discrete Fourier Transform Frequency

What is the Discrete Fourier Transform Frequency?

The Discrete Fourier Transform Frequency (DFT) is a mathematical tool used to analyze signals and data in the frequency domain. It converts a signal from its original form in the time domain to a representation in the frequency domain, allowing for the identification of specific frequencies present in the signal.

How is the DFT calculated?

The DFT is calculated by taking a finite number of samples from a signal and computing the sum of the products of each sample with complex sinusoids at different frequencies. This process is repeated for each frequency, resulting in a set of complex numbers that represent the signal in the frequency domain.

What are the applications of the DFT?

The DFT has a wide range of applications in various fields, including signal processing, image processing, data compression, and spectral analysis. It is also used in audio and video compression, as well as in solving differential equations in engineering and physics.

What is the difference between the Discrete Fourier Transform and the Fast Fourier Transform?

The Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT) are closely related, but they differ in their computational efficiency. The DFT requires O(n^2) operations, while the FFT algorithm reduces this to O(nlogn) operations, making it much faster for large data sets.

Are there any limitations of the DFT?

One limitation of the DFT is that it assumes the signal being analyzed is periodic. It also has a finite frequency resolution, which means it may not accurately represent signals with high-frequency components. Additionally, the DFT is sensitive to noise and can produce inaccurate results if the signal contains noise.

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