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Discrete Fourier Transform01:15

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Relation of DFT to z-Transform01:20

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The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
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Updated: Sep 11, 2025

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Depth Dynamics via One-Bit Frequency Probing in Embedded Direct Time-of-Flight Sensing.

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    This study introduces a novel method to transform time-of-flight (ToF) sensors into depth frequency analyzers. This enables precise measurement of high-frequency motion and transient events using lightweight, on-sensor computations.

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    Area of Science:

    • Photonics and Sensor Technology
    • Signal Processing
    • Computational Imaging

    Background:

    • Traditional time-of-flight (ToF) sensors using single-photon avalanche diodes (SPADs) aggregate photon return times, losing crucial data for dynamic depth analysis.
    • Measuring high-frequency motion and transient depth changes requires advanced signal processing that is often computationally intensive.

    Purpose of the Study:

    • To develop a method for transforming direct ToF sensors into depth frequency analyzers.
    • To enable lightweight, on-sensor computation for measuring high-frequency motion and transient depth events.
    • To extend depth dynamics analysis to time-localized detection of brief depth changes.

    Main Methods:

    • Replaced conventional discrete Fourier transforms (DFTs) with one-bit probing sinusoids generated via oversampled sigma-delta modulation for in-pixel frequency analysis.
    • Implemented lightweight, multiplier-free, and floating-point-free frequency analysis.
    • Extended analysis to Haar wavelets for time-localized detection of transient depth changes.

    Main Results:

    • Achieved noise performance comparable to full-resolution DFTs.
    • Successfully detected sub-millimeter motions exceeding 6 kHz.
    • Demonstrated localization of millisecond-scale transient depth events.
    • Validated through simulations and hardware experiments.

    Conclusions:

    • The proposed method enables a new class of compact, motion-aware ToF sensors.
    • Potential applications include industrial predictive maintenance, structural health monitoring, robotic perception, and dynamic scene understanding.
    • The approach facilitates efficient, on-sensor analysis of depth dynamics.