dft | Discrete Fourier transform | Video Utils library

My question is simple. I think I kind of understand FFT and DFT. what I dont understand is why, in Python or matlab, do we use FFT size as the number of samples? why does every sample taken in the time domain corresponds to a frequency bin in the frequency domain.

For example the Scipy's fft pack, in order to plot the spectrum of a .wav file signal we use:

Given this simple dataframe:

from my knowledge, Power Spectral Density (PSD) should stay relatively constant with the total time sampled (or aka. N-points sampled), however I have having trouble obtaining this result.

As I know from Discrete Fourier Transform (DFT), the amplitude normalization is 1/N. (e.g Amplitude Spectrum = DFT/N). However, from various sources, the PSD is defined as (DFT * DFT-conjugate / N).

How can this be possible? It is true that the Amplitude Spectrum has a 1/N normalization constant, then shouldn't the PSD have a 1/N^2 normalization constant (since DFT is proportional to N and so is its conjugate).

More specifically, I am trying to calcuated the PSD of a continuous electric field wave using the Eq. 9 of this paper. However I can't make sense of it's constants infront of the DFT since the factors of N's cancel out leaving behind only the summation of the window function squared. I tested this result and found that the PSD does not stay relatively constant with sampling size.

In summary, I have having troubles since my PSD varies with the amount of total time of the signal sampled. Any help would be great, thanks!

Hello there, hope you are all doing well. I tried to implement a Frequency Domain Laplacian Filter on Python according to this formula, which I found from a lecture note:

This is my Python function:

I want to draw black rectangles on an FFT magnitude image and apply the IFFT. I tried calculating the FFT I get 2 arrays one for the magnitude and the other for the phase after editing the magnitude image (I converted it to uint8) I don't know how to convert to the right input format for the IFFT. This the FFT code I'm using:

I have a dataset which includes some nested variables. For example, I have the following variables: the speed of a car, the existence of another car following it other_car and, if there is another car, the distance between the two cars distance. Dummy dataset:

I am creating a BIML script that will allow me to import CSV's.

However, the property Row Delimiter on the Flat File Connection Manager is somehow set to Vertical Bar, just as the Column Delimiter is. That prevents me from importing the files.

The column delimiter as a vertival bar right, I just do not get why it sets the row delimiter as vertical bar also...

Whenever I manually set the Row Delimiter to CRLF the thing works like a charm. But from BIML it is always set to the same value as the column delimiter.

I can not find where that happens....

I tried to use expressions in several ways to set the Row Delimiter but alas.....

Does anyone have any clue?

I have a table that contains filenames and some other attributes. I want to insert these records in an array in BIML so that I can loop through these files (and import them using the additional attributes).

The code to import such a file is mostly done. For now just need the part where I put the info below in an array so that I can loop through them.

I have a large number of latitude and longitude values that I would like to bin together in order to display them on a heatmap (ipyleaflet only seems to allow 2000 or so points in the heatmap and this would also be much more efficient when using big data).

I am actually using vaex, but a answer in terms of pandas is also fine.

The pandas pd.cut function seems to be helpful in terms of binning, however it produces a categorical column (category dtype) which looks like a list of all the values in the bin. Is there some way of changing this to just be an incremental number identifying each bin (thanks jezreal for that part of the answer)? I just need a bin number in order to then groupby the bin number and average (mean) on the latitude and longitude columns. I also need a count for the intensity of the heatmap entry.

For example: