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Topic: Mixed radix

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	Mixed radix FFT
		While the technique is useful for splitting the mixed radix FFT into a power-of-2 FFT and one FFT with no power-of-2 computations, it can be used recursively to implement algorithms whose size has an arbitrary number of factors.
		The mixed radix FFT is based on the factorization of a size-N FFT into two stages.
		In the center branch the mixed radix FFT is used to show how the same factorization technique can be used to implement a large power-of-2 FFT.
	www.gedae.com /SUPPORT/APPNOTES/MIXED/mixed1.html (494 words)

	Mixed radix: Definition and Links by Encyclopedian.com
		...Mixed radix Mixed radix Mixed radix numeral systems are unique in that the...can be rendered in mixed-radix notation as: $egin{bmatrix} 2, 5, 7, 45, 15, 500...The digits are written above their base, and a semicolon is used to indicate the...$
		Mixed radix numeral systems are unique in that the numerical base may vary from position to position.
		The digits are written above their base, and a semicolon is used to indicate the radix point[?].
	www.encyclopedian.com /mi/Mixed-radix.html (214 words)

	Mixed radix (Site not responding. Last check: 2007-10-19)
		Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position.
		A historical example of a mixed radix numeral system is the system of Mayan numerals, which generally used base-20, except for the second place (the "10s" in decimal) which was base-18, so that the first two places counted up to 360 (an approximation to the number of days in the year).
		Conversion of values from one mixed base to another is easily accomplished by first converting the place values of the one system into the other, and then applying the digits from the one system against these.
	nba.servegame.org /en/Mixed_radix.htm (505 words)

	ANSDIT - The letter "F" (Site not responding. Last check: 2007-10-19)
		In a floating-point representation, the numeral that is multiplied by the exponentiated implicit floating-point base to determine the real number represented; for example, a floating-point representation of the number 0.0001234 is 0.1234 E-3, where: 0.1234 is the fixed-point part and E-3 is the exponent.
		A radix notation in which the radix point is implicitly fixed in the series of digit places by some convention.
		A radix notation in which all the digit places, except perhaps the one with the highest weight, have the same radix.
	www.ncits.org /tc_home/k5htm/f1.htm (2120 words)

	Mixed radix (Site not responding. Last check: 2007-10-19)
		'''Mixed radix''' numeral systems are more general than the usual ones in that the numerical base may vary from position to position.
		When deciding which denominations to mint (and hence which radices to mix), a compromise is aimed for between a minimal number of different denominations, and a minimal number of individual pieces of coinage required to represent typical quantities.
		An example of a mixed radix numeral system in history is the system of Mayan numerals, which generally used base-20, except for the second Place (the "10s" in decimal) which was base-18, so that the first two places counted up to 360 (an approximation to the number of days in the year).
	mixed-radix.iqnaut.net (464 words)

	RFEL News and Events
		RF Engines Limited (RFEL), the supplier of high performance FPGA-based solutions, is a world leader in the creation of mixed radix cores and have implemented numerous designs for applications in communications and defence systems.
		John Summers, RFEL's CEO, explained, "Mixed Radix FFT designs are very difficult particularly where a highly efficient design is required.
		The exact specifications for 3GPP LTE have yet to be ratified, but it's been clear for sometime that mixed radix FFTs will form a fundamental element of the design, and so putting RFEL in a leadership position of being able to provide solutions immediately from its portfolio of licensable IP.
	www.rfel.com /Newseventsdetail.asp?ID=87 (422 words)

	mixed radix FFT
		point using a mixed radix fft or do most engineers use the published
		radix 4 and pad the sampled input with zeros to 16 points?
		if some one does use a mixed radix..any one care to check my 144
	www.dsprelated.com /groups/c6x/show/6063.php (57 words)

	DADiSP Products: FAQ
		Because DADiSP uses a mixed radix FFT algorithm, FFTs are not limited to signals with lengths equal to a power of two.
		The mixed radix FFT breaks the calculations into a number of steps (or loops), determined by the number of factors of the length of the input series.
		Mixed FFT Algorithm Loop 1/3 (for 47) Mixed FFT Algorithm Loop 2/3 (for 13) Mixed FFT Algorithm Loop 3/3 (for 5)
	www.dadisp.com /qa.htm (3957 words)

	Radix Sort
		The radix sort is easily made stable if a temporary array is used.
		Radix sort in base ten was very natural for humans using the card sorting machine, but any base can be used and base two is natural for computers.
		This radix exchange sort can be thought of as a variation on quick sort.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Sort/Radix (667 words)

	Re: Mixed radix arithmetic
		But, if mixed radix expressions start to be routine, someone will rethink that idea.
		BTW, I believe David mentioned that he thought that the use of base conversion in mixed expressions (in weak typed languages) should be made explicit.
		As I don't think we will be able to come up with a consistent tower of mixed datatypes, it is really the only way to go.
	grouper.ieee.org /groups/754/email/msg00708.html (587 words)

	► » mixed radix fft (radix 2 and radix 5) (Site not responding. Last check: 2007-10-19)
		I am looking for a mixed radix 2 and 5 fft algorithm in C. I have
		An algorithm of the type you are looking for is in netlib.
		Alternatively, there are a few other C codes that handle mixed
	www.iprore.com /mixed-radix-fft-radix-2-and-radix-5-2834031.html (512 words)

	Mixed Radix Algorithms.
		Mixed radix algorithms are rarely used for signal processing.
		For most signal processing applications, your far better off designing your system with Radix 2 FFT's in mind (For example, chose your sampling frequency so that a Radix 2 FFT will give you the resolution you want from a spectrum analysis).
		Another slight advantage of a Radix 4 algorithm is that with fixed point arithmetic, the most common scaling factor (root N) can be implemented simply by shifting the results right one place (dividing by 2) after each pass.
	homepages.nildram.co.uk /~ahey/T0001/PT07.HTM (1257 words)

	Info: (gsl-ref) Mixed-radix FFT routines for complex data
		- Data Type: gsl_fft_complex_wavetable This is a structure that holds the factorization and trigonometric lookup tables for the mixed radix fft algorithm.
		It has the following components: `size_t n' This is the number of complex data points `size_t nf' This is the number of factors that the length `n' was decomposed into.
		The mixed radix algorithms require additional working space to hold the intermediate steps of the transform.
	www.cims.nyu.edu /cgi-comment/info2html?(gsl-ref)Mixed-radix%2520FFT%2520routines%2520for%2520complex%2520data (948 words)

	Mixed Radix Algorithms.
		Mixed radix algorithms are rarely used for signal processing.
		For most signal processing applications, your far better off designing your system with Radix 2 FFT's in mind (For example, chose your sampling frequency so that a Radix 2 FFT will give you the resolution you want from a spectrum analysis).
		Another slight advantage of a Radix 4 algorithm is that with fixed point arithmetic, the most common scaling factor (root N) can be implemented simply by shifting the results right one place (dividing by 2) after each pass.
	www.engineeringproductivitytools.com /stuff/T0001/PT07.HTM (1257 words)

	Efficient Digital Channelisers For FPGAs The most common technique... Wideband down converter solutions The WOLA or ...
		In particular we concentrate on the requirement to use Mixed Radix FFTs.
		This means that it must be a mixed radix solution with radices of 13, 5 and factors of n.
		There is no solution of this type that will provide the required channel spacing and output sample rate without carrying out a DFT of this length, which implies a mixed radix FFT implementation.
	www.epn-online.com /page/15837/efficient-digital-channelisers-for-fpgas-mixed-radix-fft-designs.html (1276 words)

	Definition of Mixed radix
		An interesting proposal is a factorial based radix:
		This can be easily proved with mathematical induction.
		The factorial based radix is also called the factoradic.
	www.wordiq.com /definition/Mixed_radix (295 words)

	Systat Software Inc. - AutoSignal - HTML Help
		AutoSignal uses a modification of Singleton's mixed radix algorithm (R. Singleton, "An Algorithm for Computing the Mixed Radix Fast Fourier Transform", IEEE Trans.
		This algorithm is slower than the radix 2 and prime factor procedures.
		When very large primes are present, this algorithm is faster than the mixed radix procedure.
	www.systat.com /products/AutoSignal/help/?sec=1124 (370 words)

	Mixed radix . The Art of Computer Programming
		radix numeral systems are more general than the usual ones in that the numerical base may vary from position to position.
		In numeral format, each digit has its associated base attached as a subscript, and the radix point s position
		based radix, also known as factoradic: radix: 6 5 4 3 2 1 place value: 5!
	www.uk.kunsimuna.net /Mixed_radix_UK_317133_lt (538 words)

	Re: Mixed radix arithmetic
		The indication should be drawn from a Standard-define enumeration, which should include entries for "not implemented", "unitialized", and one or more "other implementation specific".
		As the possible causes may differ between the radices, I think the enumeration should represent the union of the conditions, so that the indication will survive radix conversion.
		In this sense, that a NaN encodes a condition which may indicate the radix that obtained when the condition occurred, yes, a Not a Number can have a radix, despite Dan's amusement.
	grouper.ieee.org /groups/754/email/msg00712.html (280 words)

	fprintf
		The results of mixing numbered and unnumbered argument specifications in a format string are undefined.
		In the POSIX locale, or in a locale where the radix character is not defined, the radix character shall default to a period (
		, where there is one digit before the radix character (which is non-zero if the argument is non-zero) and the number of digits after it is equal to the precision; if the precision is missing, it shall be taken as 6; if the precision is zero and no
	www.opengroup.org /onlinepubs/009695399/functions/printf.html (3736 words)

	FFT FAQ
		Also, "mixed radix" FFT's also can be done on "composite" sizes.
		For example, an FFT of size 1000 might be done in six stages using radices of 2 and 5, since 1000 = 2 * 2 * 2 * 5 * 5 * 5.
		The "radix" is the size of an FFT decomposition.
	www.dspguru.com /info/faqs/fftfaq2.htm (1074 words)

	Broad information about Scientific Astrology, Astrolgical Advice and the Elements of Astrology, by Rudolf Megert
		The basis is always the assumption that the Planets of our Solar System are nothing else but any other system we know, the eco system, the nerve system, the traffic system and so on, a system of interactive happenings.
		Sure, the prolific Psychiatrist had mixed impressions, made mixed observations and therefore found it hard to make a proper assessment.
		Psychology is an observing science, a doctor of psychology needs to assess a client by his/her behavior patterns, body language and ways of lingual expressions.
	cloud.prohosting.com /astrolge (1280 words)

	Mixed Radix FFT — www.dilloneng.com
		Mixed radix-2, 3, 5, and 7 lengths available
		Block diagram of a Parallel Mixed Radix-2/3 FFT.
		An example of one of the many Mixed Radix FFT architectures Dillon Engineering has available.
	www.dilloneng.com /fft_ip/mixed-radix-fft-ip (195 words)

	Electronic Forum - mixed radix fft (radix 2 and radix 5) (Site not responding. Last check: 2007-10-19)
		Electronic Forum - mixed radix fft (radix 2 and radix 5)
		Subject: mixed radix fft (radix 2 and radix 5)
		Subject: Re: mixed radix fft (radix 2 and radix 5)
	www.electrothree.com /detail-1314444.html (503 words)

	KISS FFT version 0.2 now does mixed radix
		KISS FFT version 0.2 now does mixed radix - Mark Borgerding -
		FFT libraries don't need to be that complicated.
		Re: KISS FFT version 0.2 now does mixed radix - Mark Borgerding -
	www.dsprelated.com /showmessage/18390/1.php (180 words)

	Systat Software Inc. - TableCurve 2D - HTML Help
		The mixed radix FFT algorithm processes any size n exactly.
		TableCurve 2D uses a modification of Singleton's mixed radix algorithm (R. Singleton, "An Algorithm for Computing the Mixed Radix Fast Fourier Transform", IEEE Trans.
		This is the recommended algorithm for most procedures within TableCurve 2D that use the FFT.
	www.systat.com /products/TableCurve2D/help/?sec=1138 (355 words)

	Ada 95 QUALITY AND STYLE Guide Chapter 3 (Part 1 of 2)
		Decimal and octal numbers are grouped by threes beginning on the left side of the radix point and by fives beginning on the right side of the radix point.
		Hexadecimal numbers are grouped by fours beginning on either side of the radix point.
		for packages that provide units of functionality that can be "mixed in" to core abstractions.
	www.grammatech.com /style_guide/sec_3a.html (4722 words)

	Mixed-radix FFT routines for complex data - GNU Scientific Library -- Reference Manual
		This is a structure that holds the factorization and trigonometric lookup tables for the mixed radix fft algorithm.
		The mixed radix algorithms require additional working space to hold the intermediate steps of the transform.
		This function allocates a workspace for a complex transform of length
	www.gnu.org /software/gsl/manual/html_node/Mixed_002dradix-FFT-routines-for-complex-data.html (868 words)

	Re: Motion to permit mixed-radix comparisons (Site not responding. Last check: 2007-10-19)
		Comparison operations can however be well-defined as primitives, and could be implemented efficiently as such, by using progressive interpretation: first deal with NaNs, Inf, zeros and signs, to reduce the comparison to same-sign non-zero finite numbers.
		Then do a coarse comparison based on logb(), and only when the values are very close would one have to resort to actual radix conversion.
		Even then there may be many early-decision cases.
	www.cs.berkeley.edu /~ejr/projects/ieee754/email/msg02519.html (390 words)

	Magic C++ - windows based cross-platform Visual C/C++ IDE for Unix/Linux/Cygwin
		You can use the Memory window to view large buffers, strings, and other data that do not display well in the Watch or Variables window.
		You can change the display radix format of variables in the QuickWatch dialog box or in the Watch window using OCTAL, DECIMAL or HEXADECIMAL etc.
		Embedded system developers are able to do remote debugging of an embedded Linux target.
	magicunix.com /product01.htm (452 words)

	Simdesign - Complex mixed-radix FFT on arbitrary length data
		By downloading the package you must agree to the terms stated in the readme.txt file.
		Singleton, "An Algorithm for Computing the Mixed Radix Fast Fourier Transform", IEEE Trans.
		This company provides highly specialised software for many imaging and audio processing tasks.
	www.simdesign.nl /fft.html (595 words)

	RFEL Press Information
		For information relating to the images, please refer to the associated technical articles
		RF Engines' Mixed Radix cores, adaptable for next generation 3GPP LTE base station applications (pdf 301K)
		New 'Matrix' range of mixed radix IP Cores
	www.rfel.co.uk /press_loggedin.asp (835 words)

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