Frequency Estimation of Sinusoidal Signals Using FFT

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Resource Overview

Estimating the frequency of a sinusoidal signal contaminated with additive white Gaussian noise via FFT involves computing the Fourier transform of x(n) to obtain the spectrum, identifying the frequency corresponding to the maximum magnitude, and calculating the mean squared error over multiple iterations. By varying the signal-to-noise ratio (SNR), simulations demonstrate that the mean squared error decreases as SNR increases, highlighting the method's robustness in noisy environments.

Detailed Documentation

This document outlines the application of the Fast Fourier Transform (FFT) to estimate the frequency of a sinusoidal signal embedded in additive white Gaussian noise. The procedure begins by computing the Fourier transform of the discrete-time signal x(n) to generate a frequency spectrum. The frequency associated with the peak magnitude in the spectrum is identified as the estimated frequency. To evaluate the estimation accuracy, the mean squared error (MSE) is calculated over multiple FFT iterations. Furthermore, by systematically adjusting the signal-to-noise ratio (SNR), simulation experiments reveal that the MSE diminishes as the SNR increases, underscoring the effectiveness of FFT-based frequency estimation in improving signal clarity under varying noise conditions.

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