Problem on symmetry property of dft in Digital signal processing || EC Academy скачать в хорошем качестве

Problem on symmetry property of dft in Digital signal processing || EC Academy

This EC Academy lecture is a hands-on problem-solving session demonstrating the powerful application of the Symmetry Property of the Discrete Fourier Transform (DFT) in Digital Signal Processing (DSP). The core of the problem is to determine the remaining DFT samples, X(5), X(6), and X(7), given the first five samples (X(0) to X(4)) of an 8-point DFT (N=8). We utilize the crucial symmetry relationship for real signals, $X(N-k) = X*(k)$, where $X*(k)$ is the complex conjugate of $X(k)$, to efficiently find the missing frequency-domain values. Furthermore, the video shows how to use the Inverse DFT (IDFT) formula and the determined DFT values to calculate the corresponding time-domain samples, such as $x(0)$, providing a complete analytical approach. This is a vital exercise for students to apply theoretical properties to simplify complex DFT calculations. Topics Covered with Timestamps: 0:00 Introduction and Problem Statement (8-point DFT, given X(0) to X(4)) 0:47 Stating the Symmetry Property of DFT: X(N-k) = X*(k) 1:27 Applying the symmetry property to calculate X(5) 2:07 Applying the symmetry property to calculate X(6) 3:00 Applying the symmetry property to calculate X(7) 4:25 Setting up the calculation for time-domain samples using IDFT 5:00 Recalling the Inverse DFT (IDFT) formula 5:38 Substituting DFT values into the IDFT formula for x(0) 6:30 Final result for the time-domain sample x(0) 6:50 Conclusion and Summary of the Solution Facebook:   / ahecacademy   Twitter:   / asif43hassan   Wattsapp: https://wa.me/919113648762 YouTube:    / ecacademy   #Subscribe, Like and Share 👉    / ecacademy   #Playlist 👇 #DigitalSignalProcessing👉    / playlist   list=PLXOYj6DUOGrpVb7_cCB1pZuGH4BFlp61B #DigitalImageProcessing👉    / playlist   list=PLXOYj6DUOGrrjyRKpD0U0bIKGOXCAOHkE #BasicElectronics👉    / playlist   list=PLXOYj6DUOGrqjdqkWSZi4we3Q3oWCvmsW #DigitalElectronics👉    / playlist   list=PLXOYj6DUOGroZA7mStdqXWQl3ZaKhyHbO #FlipFlops👉 https://www.youtube.com/playlist?list... xVBQjrEX #Opamp👉    • Плейлист   #ContolSystems👉    / playlist   list=PLXOYj6DUOGrplEjDN2cd_7ZjSOCchZuC4 #SignalsAndSyatems👉    / playlist   list=PLXOYj6DUOGrrAlYxrAu5U2tteJTrSe5Gt #DigitalCommunication👉 https://www.youtube.com/playlist?list... O76Jv2JVc7PsjM80RkeS