Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
IEEE Transactions on Computers
On Local Roundoff Errors in Floating-Point Arithmetic
Journal of the ACM (JACM)
Floating Point Fast Fourier Transform Computation Using Double Precision Floating Point Accumulators
ACM Transactions on Mathematical Software (TOMS)
Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation
Communications of the ACM
Inverses of Multivariable Polynomial Matrices by Discrete Fourier Transforms
Multidimensional Systems and Signal Processing
Fixed-point fast Hartley transform error analysis
Signal Processing
Response of model simulated weather parameters to round-off-errors on different systems
Environmental Modelling & Software
Error Analysis and Verification of an IEEE 802.11 OFDM Modem using Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Precision Attainable with Various Floating-Point Number Systems
IEEE Transactions on Computers
Journal of Computational Physics
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The fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier coefficients with a substantial time saving over conventional methods. The finite word length used in the computer causes an error in computing the Fourier coefficients. This paper derives explicit expressions for the mean square error in the FFT when floating-point arithmetics are used. Upper and lower bounds for the total relative mean square error are given. The theoretical results are in good agreement with the actual error observed by taking the FFT of data sequences.