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#fourierseries — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #fourierseries, aggregated by home.social.

  1. The Fourier transform (FT), explained in one sentence: 🔗 blog.revolutionanalytics.com/2
    \[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]

    Discrete Fourier transform (DFT):
    \[\displaystyle x_n = \sum_{k=0}^{N-1} X_k \cdot e^{-i2\pi \tfrac{n}{N}k}\]

    Inverse transform:
    \[\displaystyle X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n \cdot e^{i2\pi \tfrac{n}{N} k}\]

    #FourierTransform #FourierSeries #Transform #MathematicalTransform #Signal #SignalProcessing #Frequency #Energy #FourierAnalysis #Series #Analysis

  2. The Fourier transform (FT), explained in one sentence: 🔗 blog.revolutionanalytics.com/2
    \[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]

    Discrete Fourier transform (DFT):
    \[\displaystyle x_n = \sum_{k=0}^{N-1} X_k \cdot e^{-i2\pi \tfrac{n}{N}k}\]

    Inverse transform:
    \[\displaystyle X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n \cdot e^{i2\pi \tfrac{n}{N} k}\]

    #FourierTransform #FourierSeries #Transform #MathematicalTransform #Signal #SignalProcessing #Frequency #Energy #FourierAnalysis #Series #Analysis

  3. The Fourier transform (FT), explained in one sentence: 🔗 blog.revolutionanalytics.com/2
    \[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]

    Discrete Fourier transform (DFT):
    \[\displaystyle x_n = \sum_{k=0}^{N-1} X_k \cdot e^{-i2\pi \tfrac{n}{N}k}\]

    Inverse transform:
    \[\displaystyle X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n \cdot e^{i2\pi \tfrac{n}{N} k}\]

    #FourierTransform #FourierSeries #Transform #MathematicalTransform #Signal #SignalProcessing #Frequency #Energy #FourierAnalysis #Series #Analysis

  4. The Fourier transform (FT), explained in one sentence: 🔗 blog.revolutionanalytics.com/2
    \[\boxed{\hat{f}(\xi)=\displaystyle\int_{-\infty}^\infty e^{-i2\pi\xi t}f(t)\ \mathrm{d}t}\]

    Discrete Fourier transform (DFT):
    \[\displaystyle x_n = \sum_{k=0}^{N-1} X_k \cdot e^{-i2\pi \tfrac{n}{N}k}\]

    Inverse transform:
    \[\displaystyle X_k = \frac{1}{N} \sum_{n=0}^{N-1} x_n \cdot e^{i2\pi \tfrac{n}{N} k}\]

    #FourierTransform #FourierSeries #Transform #MathematicalTransform #Signal #SignalProcessing #Frequency #Energy #FourierAnalysis #Series #Analysis