Overlap–save method, and 15 short stories, one volume of bibliography, greatly expanded from the 1948 edition, a volume of mostly biographical material with some bibliographical material, including a section on sometime Shiel collaborator, Louis Tracy, and a final volume of essays about Shiel. The Works of M. P. Shiel The Works of M. P. Shiel is a bibliography of works by British author M. P. Shiel. The bibliography was compiled by A. Reynolds Morse. It was first published by Fantasy Publishing Company, Inc. in 1948 in an edition of 1,000 copies. Morse later revised the book as volumes II & III of a 	The Works of M. P. Shiel
18793374	Overlap–save method Overlap–save method In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal formula_1 and a finite impulse response (FIR) filter formula_2: where for m" outside the region . This article uses common abstract notations, such as formula_3 or formula_4 in which it is understood that the functions should be thought of in their totality, rather than at specific instants formula_5 (see Convolution#Notation). The concept is to compute short segments of "y"["n"] of an arbitrary length "L", and concatenate the segments together. Consider a segment that begins at  n = "kL" + "M", for any integer "k", and define: Then, for formula_8, and equivalently formula_9, we can write: With the substitution formula_11, the task is reduced to computing formula_12 for formula_13. These steps are illustrated in the first 3 traces of Figure 1, except that the desired portion of the output (third trace) corresponds to 1  ≤   ≤  ""'L". If we periodically extend "x"["n"] with period "N"  ≥  "L" + "M" − 1, according to: the convolutions  formula_15  and  formula_16  are equivalent in the region formula_17. It is therefore sufficient to compute the N-point circular (or cyclic ) convolution of formula_18 with formula_19  in the region [1, "N"].  The subregion ["M" + 1, "L" + "M"] is appended to the output stream, and the other values are discarded.  The advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem: where: Pseudocode. ("Overlap-save algorithm for linear convolution") Efficiency considerations. When the DFT and IDFT are implemented by the FFT algorithm, the pseudocode above requires about complex multiplications for the FFT, product of arrays, and IFFT. Each iteration produces output samples, so the number of complex multiplications per output  sample is about: For example, when M=201 and N=1024, equals 13.67, whereas direct evaluation of would require up to 201 complex multiplications per output sample, the worst case being when both x and h are complex-valued. Also note that for any given M, has a minimum with respect to N. Figure 2 is a graph of the values of N that minimize for a range of filter lengths (M). Instead of , we can also consider applying to a long sequence of length formula_20 samples. The total number of complex multiplications would be: Comparatively, the number of complex multiplications required  by the pseudocode algorithm is: Hence the "cost" of the overlap–save method scales almost as formula_23 while the cost of a single, large circular convolution is almost formula_24. Overlap–discard. "Overlap–discard" and "Overlap–scrap" are less commonly used labels for the same method described here. However, these labels are actually better (than "overlap–save") to distinguish from overlap–add, because both methods "save", but only one discards. "Save" merely refers to the fact that "M" − 1 input (or output) samples from segment "k" are needed to process segment "k" + 1. Extending overlap–save. The overlap–save  algorithm can be extended to include other common operations of a system: Overlap–save method In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal formula_1 and a finite impulse response (FIR) filter formula_2: where for "m" outside the region . This article uses common abstract notations, such as formula_3 or formula_4 in which it is understood that the functions should be thought of in their totality, rather than at specific instants formula_5 (see Convolution#Notation). The concept is to compute short segments of "y"["n"] of an arbitrary length