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Gilles
Gilles
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I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points.

I want to use FFT to calculate PSD estimate. FFT gives me a set of complex numbers that I want to transform into the PSD values. I am aware of the fact that only the first N/2 + 1$N/2 + 1$ values are useful, and that the other half are complex conjugates of the first half.

  1. I know that I will need to take the magnitude squared of each (useful) complex number the FFT gave me in order to find the PSD values. I also found out that I should incorporate some scaling/normalizing of the result. It is at this point that I am unsure. In some of the replies to similar questions it is said that the magnitude squared should be multiplied by 1/N$1/N$ only, while in others it is said that it should be multiplied by 1 / (N*Fs)$1 / \left(N\cdot F_s\right)$. I have not been able to figure out which of these two should be used when. Can anyone explain?

  2. The sampling frequency of my signal is 128 Hz$128\textrm{ Hz}$. The length of the signal to be transformed is 256$256$ samples. In this case I found out that the distance between the resultant values of the FFT (or PSD values) should be 128/256 = 0.5 Hz$128/256 = 0.5\textrm{ Hz}$. Is that correct?

  3. The original signal is in uV$\mu V$. In what values will the result of the PSD be? Is it uV^2$\mu V^2$ or uV^2 / Hz$\mu V^2 /\textrm{ Hz}$? (There might be a connection here with what I am asking in 1), am I right?)

I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points.

I want to use FFT to calculate PSD estimate. FFT gives me a set of complex numbers that I want to transform into the PSD values. I am aware of the fact that only the first N/2 + 1 values are useful, and that the other half are complex conjugates of the first half.

  1. I know that I will need to take the magnitude squared of each (useful) complex number the FFT gave me in order to find the PSD values. I also found out that I should incorporate some scaling/normalizing of the result. It is at this point that I am unsure. In some of the replies to similar questions it is said that the magnitude squared should be multiplied by 1/N only, while in others it is said that it should be multiplied by 1 / (N*Fs). I have not been able to figure out which of these two should be used when. Can anyone explain?

  2. The sampling frequency of my signal is 128 Hz. The length of the signal to be transformed is 256 samples. In this case I found out that the distance between the resultant values of the FFT (or PSD values) should be 128/256 = 0.5 Hz. Is that correct?

  3. The original signal is in uV. In what values will the result of the PSD be? Is it uV^2 or uV^2 / Hz? (There might be a connection here with what I am asking in 1), am I right?)

I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points.

I want to use FFT to calculate PSD estimate. FFT gives me a set of complex numbers that I want to transform into the PSD values. I am aware of the fact that only the first $N/2 + 1$ values are useful, and that the other half are complex conjugates of the first half.

  1. I know that I will need to take the magnitude squared of each (useful) complex number the FFT gave me in order to find the PSD values. I also found out that I should incorporate some scaling/normalizing of the result. It is at this point that I am unsure. In some of the replies to similar questions it is said that the magnitude squared should be multiplied by $1/N$ only, while in others it is said that it should be multiplied by $1 / \left(N\cdot F_s\right)$. I have not been able to figure out which of these two should be used when. Can anyone explain?

  2. The sampling frequency of my signal is $128\textrm{ Hz}$. The length of the signal to be transformed is $256$ samples. In this case I found out that the distance between the resultant values of the FFT (or PSD values) should be $128/256 = 0.5\textrm{ Hz}$. Is that correct?

  3. The original signal is in $\mu V$. In what values will the result of the PSD be? Is it $\mu V^2$ or $\mu V^2 /\textrm{ Hz}$? (There might be a connection here with what I am asking in 1), am I right?)

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seashrimp
seashrimp
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PSD estimate using FFT - scaling and units

I know that similar questions have already been asked – I have read the answers, yet I am still not sure if I understand the topic properly at some points.

I want to use FFT to calculate PSD estimate. FFT gives me a set of complex numbers that I want to transform into the PSD values. I am aware of the fact that only the first N/2 + 1 values are useful, and that the other half are complex conjugates of the first half.

  1. I know that I will need to take the magnitude squared of each (useful) complex number the FFT gave me in order to find the PSD values. I also found out that I should incorporate some scaling/normalizing of the result. It is at this point that I am unsure. In some of the replies to similar questions it is said that the magnitude squared should be multiplied by 1/N only, while in others it is said that it should be multiplied by 1 / (N*Fs). I have not been able to figure out which of these two should be used when. Can anyone explain?

  2. The sampling frequency of my signal is 128 Hz. The length of the signal to be transformed is 256 samples. In this case I found out that the distance between the resultant values of the FFT (or PSD values) should be 128/256 = 0.5 Hz. Is that correct?

  3. The original signal is in uV. In what values will the result of the PSD be? Is it uV^2 or uV^2 / Hz? (There might be a connection here with what I am asking in 1), am I right?)