Duality property of DFT in Digital Signal Processing || EC Academy скачать в хорошем качестве

Duality property of DFT in Digital Signal Processing || EC Academy

his EC Academy lecture covers the essential Duality Property of the Discrete Fourier Transform (DFT), a powerful concept in Digital Signal Processing (DSP). The Duality Property illustrates a symmetric relationship: if the DFT of a time-domain signal $x(n)$ is $X(k)$, then the DFT of the frequency-domain signal, treated as a time-domain sequence $X(n)$, results in a time-reversed and scaled version of the original time-domain signal, $N \cdot x((-k) \text{ mod } N)$. We provide a rigorous, step-by-step derivation and proof of the relationship This property is key to understanding the deep symmetry inherent in the Fourier analysis of discrete signals and is fundamental for transforming frequency-domain concepts back into the time domain. Topics Covered with Timestamps: 0:00 Introduction to the Duality Property of DFT 0:13 Statement of the Duality Property 1:25 Setting up the proof using the DFT and Inverse DFT (IDFT) definitions 1:48 Replacing the variables (k by n, n by k) in the IDFT formula 2:24 Simplifying the resulting equation 3:49 Comparing the derived equation (Equation 1) with the IDFT definition (Equation 2) 4:21 Final mathematical derivation and conclusion 4:50 Summary of the Duality Property #DualityProperty #DFTProperty #DiscreteFourierTransform #DSP #DigitalSignalProcessing #ECacademy #DFTSymmetry #DualityTheorem #EngineeringConcepts #ECE Follow EC Academy on Facebook:   / ahecacademy   Twitter:   / asif43hassan   Wattsapp: https://wa.me/919113648762 YouTube:    / ecacademy   #Subscribe, Like and Share 👉    / ecacademy   #Playlist 👇 #DigitalSignalProcessing 👉    • Digital signal processing Lecture Series   #DigitalImageProcessing 👉    • Digital Image Processing  Complete Lecture...   #BasicElectronics 👉    • Basic Electronics | Complete Foundation Co...   #DigitalElectronics 👉    • Плейлист   #FlipFlops 👉    • Плейлист   #Opamp 👉    • Плейлист   #ContolSystems 👉    • Control Systems Tutorial Series | GATE & U...   #SignalsAndSyatems 👉    • Signals & Systems | Complete Lecture Serie...   #DigitalCommunication 👉    • Digital Communication