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Core - Electrical Engineering

    Chapter 17

    The Fourier Transform

    17.1 : Continuous -time Fourier Transform01:11

    17.1 : Continuous -time Fourier Transform

    The Fourier series is an effective tool for representing periodic functions like a train of square waves. Consider a pulse-train waveform consisting of a ...

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    17.2 : Basic signals of Fourier Transform01:07

    17.2 : Basic signals of Fourier Transform

    Among the key elements of the Fourier Transform, the sinc function is unique in that it equals 1 when its argument is zero and exhibits even symmetry. In ...

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    17.3 : Properties of Fourier Transform I01:21

    17.3 : Properties of Fourier Transform I

    In radio broadcasting, Fourier Transform properties are applied in simultaneous multi-channel transmission, adjusting audio clip speeds, live broadcast ...

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    17.4 : Properties of Fourier Transform II01:24

    17.4 : Properties of Fourier Transform II

    The Frequency Shifting property of Fourier Transforms states that a shift in the frequency domain corresponds to a phase shift in the time domain, ...

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    17.5 : Parseval's Theorem for Fourier transform01:15

    17.5 : Parseval's Theorem for Fourier transform

    Parseval's theorem is a principle used in signal processing to calculate the energy of a signal. It allows the computation of the same energy value ...

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    17.6 : Discrete-time Fourier transform01:26

    17.6 : Discrete-time Fourier transform

    The Discrete-Time Fourier Transform is a variant of the Fourier transform applied to a discrete-time signal. This transform replaces the integral in the ...

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    17.7 : Properties of DTFT I01:24

    17.7 : Properties of DTFT I

    Consider two discrete-time signals, each with their respective Discrete-Time Fourier Transforms DTFTs. The signals are first multiplied by constants a and ...

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    17.8 : Properties of DTFT II01:24

    17.8 : Properties of DTFT II

    Consider a discrete-time Fourier transform (DTFT) pair, differentiate both sides with respect to Ω, and then multiply by j. The right-hand side ...

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    17.9 : Discrete Fourier Transform01:15

    17.9 : Discrete Fourier Transform

    Consider a vibration sensor that continuously captures data in the form of a continuous time-dependent signal. However, in reality, the sensor can only ...

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    17.10 : Fast Fourier Transform01:10

    17.10 : Fast Fourier Transform

    The Fast Fourier Transform, FFT, is a computational algorithm for calculating the Discrete Fourier Transform by breaking the calculations into smaller, ...

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