Simultaneous Computation of Discrete Fourier Transforms for Two N-Point Real Sequences Using a Single N-Point DFT
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Resource Overview
Develop a MATLAB function that utilizes a single N-point discrete Fourier transform (DFT) to concurrently compute the DFTs of two N-point real-valued sequences, and compare the results with those obtained from applying two separate N-point DFT calculations directly.
Detailed Documentation
This MATLAB function is designed to compute the discrete Fourier transform of an N-point real-valued sequence and compare the outcome with results generated by a standard N-point DFT implementation. Additionally, the function enables simultaneous calculation of the DFT for another N-point real sequence, effectively performing dual real-sequence DFT computations in one operation. The implementation leverages the conjugate symmetry property of real-valued signals' DFTs, allowing efficient packing of two real sequences into one complex sequence for joint processing. Key algorithmic steps include: combining the two real sequences as real and imaginary parts of a complex sequence, applying a single FFT (Fast Fourier Transform), and extracting individual DFT results using symmetry properties and post-processing operations like complex conjugation and frequency-shifting.
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