FFT coefficients and frequencies

In summary, The conversation discusses the process of completing a table by determining the frequencies associated with FFT values for a computation of discrete Fourier Transform. The participant is seeking help with understanding how the FFT coefficients relate to normalized and real frequencies. They suggest that the real frequency is the frequency associated with each row in Excel and provide examples of frequencies for different values of k.
  • #1
smcmon
1
0

Homework Statement



The following is the output of a 16 point computation of the discrete Fourier Transform for data taken at 10 kHz. Complete the table below by determining the frequencies associated with each of the FFT values.

I attached an Excel workbook with the table.

Homework Equations



This is what I need help with. I need help with how the FFT coefficients relate to normalized and real frequencies.

The Attempt at a Solution



I need help with understanding FFT so I have not gotten this far.
 

Attachments

  • FFT problem.xls
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  • #2
I can tell you how FFT's work and what the numbers mean.
However, I do not know what is expected exactly for a "Frequency normalized" or the "Real frequency".

Do you have definitions from your book for those?

I'd guess that the real frequency is the frequency associated with each row in Excel.
So k = 0 has frequency 0 Hz
k=1 has freq 10 kHz
k=2 has freq 20 kHz
and so forth.
 

Related to FFT coefficients and frequencies

1. What are FFT coefficients and frequencies?

FFT coefficients and frequencies are mathematical terms used in signal processing to analyze the frequency components of a signal. FFT stands for Fast Fourier Transform, which is a mathematical algorithm used to convert a signal from its original time domain representation to a frequency domain representation. Coefficients refer to the amplitude or strength of each frequency component, while frequencies refer to the different frequencies present in the signal.

2. How are FFT coefficients and frequencies calculated?

FFT coefficients and frequencies are calculated using the Fast Fourier Transform algorithm, which involves breaking down a signal into its individual frequency components and determining their amplitude or strength. This is done by multiplying the signal by a complex sinusoidal wave with a specific frequency and then summing up these products for all frequencies. The result is a set of coefficients that correspond to the different frequencies in the signal.

3. What is the importance of FFT coefficients and frequencies?

FFT coefficients and frequencies are important because they allow us to analyze the frequency components of a signal and identify any patterns or anomalies. This is useful in various fields such as signal processing, audio and image processing, and data analysis. By understanding the frequencies present in a signal, we can gain insights and make informed decisions about the data.

4. Can FFT coefficients and frequencies be used for noise reduction?

Yes, FFT coefficients and frequencies can be used for noise reduction. By analyzing the frequency components of a signal, we can identify and filter out any unwanted noise. This is done by setting a threshold for the coefficients and frequencies and removing any values that fall below this threshold. This process is known as spectral subtraction and is commonly used in audio and image denoising.

5. Are FFT coefficients and frequencies affected by the length of the input signal?

Yes, FFT coefficients and frequencies can be affected by the length of the input signal. The length of the input signal determines the resolution of the frequency domain representation, meaning that a longer signal will result in a more detailed analysis of the frequency components. However, the overall shape and characteristics of the frequency spectrum remain the same regardless of the signal length.

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