Transformada Discreta de Fourier | 11/37 | UPV

Title: Discrete Fourier Transform Description: Definition of the discrete Fourier transform, importance of windowing. Camacho García, A. (2009). Discrete Fourier Transform. https://riunet.upv.es/handle/10251/4856 Automatic description: In this video, a professor from the communications department of a polytechnic university in Valencia explains the Discrete Fourier Transform (DFT). He begins by defining the DFT and its relationship to the continuous Fourier Transform, highlighting that while the latter is a continuous complex function of a real variable, the DFT is applied to discrete signals and generates another discrete signal as a result. To calculate the DFT, two conditions must be met: the signal must be zero for any negative value of n and for values ​​of n greater than the number of points to be calculated minus one. Furthermore, it introduces the formula for calculating the Fourier Transform (FT) and the Inverse Fourier Transform, showing how to recover the original sequence in the time domain from its transform. Next, it explains the concept of windowing, which is used to limit the time of a discrete signal that does not meet the conditions for calculating the FT by means of a window, which in this case is rectangular. It describes how applying a window in the frequency domain produces a circular convolution that affects the sharpness of the resulting spectrum; a wider spectrum is associated with narrower windows and vice versa. Finally, it illustrates how to calculate the FT using MATLAB with the 'fft' command. It provides an example with a discrete signal and shows how the FT is a sample of the Fourier Transform and how to correctly represent the magnitude of the obtained FT. It concludes by explaining the interrelationship between the FT, the continuous transform, the effects of windowing, and practical exercises with MATLAB. Author: Andrés Camacho García Course: This video is 23/51 of the course Signal Processing in Communications | Universitat Politècnica de València (UPV).    • Curso Tratamiento de señales en comunicaci...   Course: This video is 11/37 of the course Signal and Communication Theory.    • Teoría de las señales y las comunicaciones   Universitat Politècnica de València UPV: https://www.upv.es More videos at:    / valenciaupv   Access our MOOCs: https://upvx.es #Fourier transform #Discrete signals #Decimation #Interpolation #Sampling