it is to be understood that the following description of examples of implementations are given only for the purpose of illustration and are not to be taken in a limiting sense . the partitioning of examples in function blocks , modules or units shown in the drawings is not to be construed as indicating that these function blocks , modules or units are necessarily implemented as physically separate units . functional blocks , modules or units shown or described may be implemented as separate units , circuits , chips , functions , modules , or circuit elements . one or more functional blocks or units may also be implemented in a common circuit , chip , circuit element or unit . in fig1 , depicted is an example sound system 100 , implementing an example embodiment of the ses ( the ses 101 ), which is transmitting sound waves 104 and 106 to a person 102 wearing headphones 103 . these sound waves 104 and 106 if measured at the person 102 are representative of a respective direct hrtf and indirect hrtf produced by the ses 101 . for the most part , the person 102 receives the sound waves 104 and 106 at each respective ear 114 and 116 by way of the headphones 103 . the respective direct and indirect hrtfs that are produced from the ses 100 are specifically a result of one or more sum and cross filters of the ses 100 , where the one or more sum and cross filters are derived from known direct and indirect hrtfs . regarding deriving the sum and cross filters from the known direct and indirect hrtfs , a designer of the filters can find the known hrtfs from a source such as the publicly available database found at the institute de recherche et coordination acoustique / musique , paris , france ( ircam ). an advantage of deriving the sum and cross filters from known direct and indirect hrtfs found through ircam is that these known hrtfs contain measured data from a significant number of tested individuals , not a simulated person . additionally , in using this database or another source of known direct and indirect hrtfs , a designer of the sum and cross filters can model and then parameterize the sum and cross filters , so that individual listeners can adjust particular parameters to fine tune the output of the ses . as described in detail subsequently , a method used by a designer of the ses ( and more particularly the sum and cross filters ) can include the transformation of the known direct and indirect hrtfs to the sum and cross filters and the parameterization of the sum and cross filters . also , in addition to describing design of the sum and cross filters , this disclosure will present example modules of example embodiments of the ses . fig2 is a signal flow diagram of an example module 200 of an embodiment of the ses having sum and cross filters 204 and 206 for transforming an audio signal , which is inputted at an input 202 , into direct and indirect hrtfs that are outputted at respective outputs 208 and 210 . in short , the example module 200 performs the function of transforming an audio output signal of a sound system to direct and indirect hrtfs . as suggested above , the example module 200 receives the audio output signal of the sound system at the input 202 . the input 202 is connected to the sum filter 204 , which is connected to the cross filter 206 . additionally , the ses multiplies , e . g ., by a factor of 2 , the filtered signal from the sum filter 204 , and then , the ses subtracts the cross filter output from the product of the multiplication . this results in the direct hrtf . the signal outputted by the cross filter represents the indirect hrtf . finally , respective outputs 208 and 210 output the direct and the indirect hrtf . further , the module 200 can be combined with other audio signal processing modules to model the filters , and eventually the ses can output , via loudspeakers or headphones , enhanced sound waves representative of the hrtfs . regarding the sum filter 204 , when applied to an audio signal it can provide spectral modifications so that such qualities of the signal are substantially similar for both ears of a listener . this filter can also eliminate undesired resonances and / or undesired peaking possibly included in the frequency response of the audio signal . as for the cross filter 206 , when applied to the audio signal it provides spectral modifications so that the signal is acoustically perceived by a listener as coming from a predetermined direction or location . this functionality is achieved by adjustment of head shadowing . in both cases , it may be desired so that such modifications are unique to an individual listener &# 39 ; s specific characteristics . to accommodate such a desire , both the sum and cross filters 206 and 204 are designed so that the frequency responses of the filtered audio signals are less sensitive to listener specific characteristics . further , with respect to design of the sum and cross filters , fig3 depicts an example method 300 for developing sum and cross transfer functions for respective sum and cross filters . in general , the method 300 teaches transforming known direct and indirect hrtfs to the sum and cross transfer functions , and then eventually parameterizing the sum and cross functions . also , the method 300 can include steps for further simplifying the sum and cross transfer functions as well . furthermore , the method 300 for deriving the sum and cross transfer functions from known direct and indirect hrtfs may include additional steps or modules that are commonly performed during signal processing that are not depicted in fig3 , such as moving data within memory and generating timing signals . also , these steps can be performed with more steps or functions in parallel . the method 300 begins at a step 302 , where a design system normalizes the direct and indirect hrtfs . normalization can occur by subtracting a measured frontal hrtf , which is the hrtf at 0 degrees , from the indirect and direct hrtf . this form of normalization is commonly known as “ free - field normalization ,” because it typically eliminates the frequency responses of test equipment and other equipment used for measurements . this form of normalization also ensures that timbres of respective frontal sources are not altered . in fig4 , depicted is a graph of measured known direct and indirect hrtfs prior to being normalized at the step 302 . fig5 , depicts a graph of the measured direct and indirect hrtfs after the normalization at the step 302 . in these graphs and a number of subsequently described graphs , the angle in which the signal source outputs the hrtfs with respect to the listener is 45 degrees . next , at a step 304 , the design system performs a smoothing function on the normalized direct and indirect hrtfs . additionally , at the step 304 , the design system can limit the normalized hrtfs to a particular frequency band . this limiting of the hrtfs to a particular frequency band can occur before or after the smoothing function . specifically , a frequency band that cuts off peaks at 15 khz has been discovered to be advantageous . an example of the smoothing function , which can be in the logarithmic frequency domain a ( 1 : n ) can be carried out in accordance with the following matlab instructions . for the sake of convenience , this function and following functions presented using the matlab syntax ; however , such function could be taught using other known programming languages . in the preceding instructions : “ n ” represents the number of frequency samples ; “ sm ” represents a smoothing coefficient ( typically sm = 1 . 1 ); and above the frequency band that cuts off peaks , the values of function “ a ” are replaced by constants identical with the cutoff frequency . in fig5 , depicted is a graph of the measured direct and indirect hrtfs after normalization . fig6 depicts a graph of the measured direct and indirect hrtfs after the design system performs the above matlab instructions or similar processor executable instructions . also , fig6 depicts a graph of the measured direct and indirect hrtfs after normalization , smoothing , and clipping . next , at a step 306 , the design system performs the transformation from the direct and indirect hrtfs to the sum and cross transfer functions . specifically , at the step 306 , the design system computes the arithmetic average of the direct hrtf and the indirect hrtf that results in the sum transfer function . also , the design system divides the indirect hrtf by the sum function that results in the cross transfer function . the relationship between these transfer functions is described by the following equations ; where h d = the direct hrtf , h i = the indirect hrtf , h s = the sum transfer function , and h c = the cross transfer function . h s =( h d + h i )/ 2 h c = h i / h s with respect to fig7 , depicted is a graph of the measured sum and cross transfer functions after being transformed from the direct and indirect hrtfs . apparent from fig7 , the sum function is relatively flat over a large frequency band in the case where the source angle is 45 degrees . it has also been discovered with regard to enhancing the sound perceived by a listener , that the sum transfer function for the most part corrects the timbre , and the cross function corrects the head shadowing , where head shadowing refers to a quality corresponding to location of the sound wave sources . next , at a step 308 , the design system performs a low order approximation on the sum and cross transfer functions . to perform the low order approximation , the design system can use a recursive linear filter , such as a combination of cascading biquad filters . an example implementation using cascading biquad filters is represented by the following matlab instructions . the first set of matlab instructions represents high shelving filters with the parameters “ f ” ( representing corner frequency ), “ q ” ( representing quality factor ), and “ a ” ( representing gain in db ). a sample rate is denoted by “ fs ”, and can be 44 . 1 khz , 48 khz , or another sample rate . such filters produce a numerator polynomial “ bz ”, and a denominator “ az ”. the second set of matlab instructions represents peak / notch filters with the parameters “ f ” ( representing notch frequency ), “ q ” ( representing quality factor ), and “ a ” ( representing gain in db ). such filters produce polynomials bn and an . in fig8 , depicted is a graph of the measured sum and cross transfer functions after the design system performs the above matlab instructions or similar processor executable instructions . also , fig8 is graph of the measured cross transfer functions after low - order approximation , where the source angle is 45 degrees . also , the cross transfer function depicted in fig8 is approximated by a peak filter and a high shelving filter . further , in some embodiments , approximations can be made with multiple peak filters and multiple shelving filters or other types of filters using biquads . with respect to the sum transfer function , peak and shelving filters are not required considering the sum function is relatively flat over a large frequency band where the sound source angle is 45 degrees with respect to a listener . also , for this reason a sum filter is not necessary when converting an audio signal outputted from a source positioned 45 degrees from the listener . as depicted in fig1 , sum filters are absent from the transformation of the audio signals coming from sources each having a 45 degree source angle . alternatively , sum filters equaling a constant 1 value could be added to the implementation depicted in fig1 and similar outputs would occur at the outputs labeled “ l ” and “ r ”. finally , at a step 310 and after one or more iterations of the steps 302 , 304 , 306 , and 308 , the design system determines one or more parameters across one or more of the resulting sum transfer functions and cross transfer functions that are common to the one or more of the resulting sum transfer functions and cross transfer functions . for example , in performing the method 300 over a number of hrtf pairs from ircam , it was found that q factor values of 0 . 6 , 1 , and 1 . 5 where common amongst the resulting notch filter in the 45 degrees cross function approximation . therefore , in an implementation of the ses a switch can be included that allows a user of the ses to select between various q factor values , such as 0 . 6 , 1 , and 1 . 5 at a source angle of 45 degrees . such finding are found in fig9 , which shows a histogram of the q factor of a notch filter section of the cross filter for a source angle of 45 degrees . depicted are test persons versus found q factor values . for example , there are eleven listeners with a q factor of 1 . 5 . by allowing selection of the q factor value , the ses provides listeners to fine tune the audio signal . for example , on a mobile device , such as an mp3 player or a smart phone , a user , via the ses , could select a desired q factor from a touchscreen or a mechanical switch . further , by minimizing the number of options , such as limiting parameterization to three options , the complexity of fine - tuning a user &# 39 ; s listening experience is reduced . another parameter having common results observed from running the method 300 , is the frequency of the notch filter section of the cross filter for a source angle of 45 degrees . it has been found by the design system , at a source angle of 45 degrees , that typically the desired filter has a notch frequency of 1275 hz . fig1 shows such findings . the histogram shows only one maximum , as opposed to three local maxima in fig9 . hence this parameter can be left constant and inaccessible for possible fine tuning , thereby reducing complexity . moreover , if we take the median values of each parameter mentioned above , we obtain filter responses such as those depict in fig1 . specifically fig1 shows the individual responses for 50 test subjects of the cross filter having a source angle of 45 degrees . typical sum and cross transfer functions obtained through steps 302 , 304 , 306 , 308 , and 310 are depicted in fig1 - 14 ( transfer functions for source angles 45 , 90 , and 135 degrees , respectively ). the transfer functions of fig1 - 14 can be used to render a set of surround sound loudspeakers or sound sources after transformation by an embodiment of the ses . for example , front stereo sound sources can be configured at +/− 45 degrees , side surround sources can be configured at +/− 90 , and rear surround sources can be configured at +/− 135 degrees . note again that the sum responses for the frontal renderings are flat ( see fig1 ). therefore , the results in binaural reproduction have very low coloration or altering of the original spectral content or timbre . referring back to the ses , fig1 is a signal flow chart that depicts an example module 1500 of an embodiment of the ses . the module 1500 is loosely based on the module 200 found in fig2 , with additions of interaural delays for source angles of 45 , 90 , and 135 degrees ( labeled “ t 45 ”, “ t 90 ”, and “ t 135 ”, respectively ). these delay filters can have typical samplings of 17 samples , 34 samples , and 21 samples , respectively , at a sample rate of 48 khz . the delay filters simulate the time a sound wave takes to reach one ear after it first reaches the other ear . the other components of the module 1500 can transform audio signals from one or more sources to a binaural format , such as direct and indirect hrtfs . specifically , in fig1 , module 1500 transforms audio signals from a 6 - channel surround sound system to direct and indirect hrtfs outputted by right and left outputs of headphones ( labeled “ hr ” and “ hl ” respectively ). these signals outputted by the headphones will include the typically perceived enhancements of 6 - channel surround sound without unwanted artifacts . also with respect to each output of the headphones respective sets of summations are included to sum three input pairs of 6 - channel surround sound . the six audio signal inputs include left , right , left surround , right surround , left rear surround , and right rear surround ( labeled “ l ”, “ r ”, “ ls ”, “ rs ”, “ lrs ”, and “ rrs ”, respectively ). also depicted by fig1 are sum and cross filters for source angles of 45 , 90 , and 135 degrees ( labeled “ hs 90 ”, “ hs 135 ”, “ hc 45 ”, “ hc 90 ”, and “ hc 135 ”, respectively ). as noted above , sum filters are absent from the transformation of the audio signals coming from sources each having a 45 degree source angle . alternatively , sum filters equaling a constant 1 value could be added to the implementation depicted in fig1 and similar outputs would occur at the outputs labeled “ l ” and “ r ”. also , alternatively , embodiments of the ses could employ other filters for sources that have other source angles , such as 30 , 80 , and 145 degrees . further , the ses or an electronic device containing the ses could store , in memory , various sum and cross filters for different source angles , so that such filters are selectable by end users . in such implementations , listeners can adjust the angles and simulated locations from which they perceive sound . referring back to the filters depicted in fig1 , from the method 300 for designing sum and cross filters , the following table 1 of filter parameters have been determined for transforming frequency responses from a 6 - channel surround sound system to headphones . in table 1 , two parameters have been identified as sufficient for individual tuning : q factor , “ q ” of the shelving section of the hc 45 filter to optimize front localization ; and gain , “ a ” of the first notch filter of the hc 135 filter to tune localization of the rear surround channels . in fig1 , depicted is a block diagram that depicts an example module 1600 of an embodiment of the ses . the module 1600 combines a distance renderer module 1602 with a parametric binaural module 1604 ( such has the module 1500 of fig1 ) and a headphone equalizer module 1606 . specifically , the module 1600 could be implemented for transformation of audio signals from 6 - channel surround to direct and indirect hrtfs for headphones . this is because the module 1600 includes six initial inputs , and right and left outputs for headphones . with respect to the distance and location rendering , the binaural model of the module 1604 provides directional information , but sound sources still appear very close to the head of a listener . this is especially the case if there is not much information with respect to the location of the sound source ( e . g ., dry recordings are typically perceived as being very close to the head or even inside the head of a listener ). the distance renderer module 1602 limits such unwanted artifacts . as described in fig1 , the distance renderer module comprises six delay lines , one per each of the initial input signals , respectively . in an embodiment of the ses , one or more tapped delay lines can be used . as for output of each delay line , there are six with each output representing one of the six initial inputs , respectively , as depicted in fig1 . further , the distance renderer module 1602 provides for summing its six outputs to be inputted into the parametric binaural module 1604 , as taught by fig1 and 17 . finally , the headphone equalizer module 1606 , which follows the parametric binaural module 1604 to further reduce coloration and improve quality of rendered hrtfs and localization . in fig1 , a schematic of one of the delay lines of fig1 is shown in detail . in embodiments where the distance renderer module includes tapped delay lines , such lines can store approximately 5000 samples for 100 ms delay at a 48 khz sample rate , and the total number of taps can be between 50 and 100 . the taps can be arranged with summations that feed into one of three absorption filters ( labeled “ filt 1 ”, “ filt 2 ”, “ filt 3 ”), respectively . also , included in one of the delay lines is a direct path between each of the lines input and output ( labeled “ in_l ” and “ out_l ”, respectively ). as shown , there is one input per line and six outputs , where five of the outputs correspond to a summation of the outputs of the three absorption filters . one benefit of these delay lines is to generate a set of room reflections that would occur if a listener were listening to sound waves outputted from loudspeakers in a room . a greater number of taps are beneficial , as to simulate as many reflected signal sources of the room as possible . the parameters of the distance renderer can be determined with ray - tracing or geometric ( mirror image ) methods . with respect to fig1 - 22 , depicted are two graphs and two signal flow to charts that illustrate an alternative benefit of the ses besides transforming sound system audio signals to direct and indirect hrtfs . this benefit being the capability to enhance loudspeaker outputs as well . the ses or binaural techniques disclosed can also widen and enhance a stereo image without adding unwanted artifacts . for example , the ses or techniques disclosed can simulate a stereo image portraying loudspeakers being virtually beyond their physical location . such an application would be helpful for listening to loud speakers in a small room , where without enhancements the experience can be exhausting to a listener . in fig1 , depicted is a general approach to stereo widening . a monaural source 1902 is to be arranged beyond a left and right loudspeaker 1904 and 1906 , respectively . the loudspeakers 1904 and 1906 output sound waves that radiate into a room before they reach the ears , which are modeled simplistically to simulate sound waves having direct and indirect paths . the sound waves having indirect paths to the ears can be simulated by a pair of cross filters 1908 and 1910 . from this model , a design system can develop input filters 1912 and 1914 (“ s ” and “ d ”, respectively ) where sound waves perceived by the ear are characterized by a new direct path 1916 , which is again set to one , and a new cross path 1918 , which corresponds to wider source angles than those portrayed by the pair of cross filters 1908 and 1910 . with given filter responses from the new cross path 1918 (“ pc ”) and the cross filters 1908 and 1910 (“ hc ”), the following transfer functions can be obtained from fig1 . the frequency responses of the filters “ s ” and “ d ” are graphed in fig2 and 21 , respectively , and the following equations represent the filters . an example of such an application could use the cross filters described above . for example , applying the hc 90 filter for pc and the hc 45 filter for hc , the application of the ses can achieve a widening effect from initially 45 degrees ( which is the actual speaker location ) to 90 degrees ( which is a virtual location ). furthermore , the scheme of fig1 can be used to simulate a stereo or surround sound system . for example , in fig2 , depicted is a scheme for a stereo system employing the aforementioned design techniques . in this scheme for a stereo system , the parametric binaural model or ses derives the s and d filters . it will be understood , and is appreciated by persons skilled in the art , that one or more processes , sub - processes , or process steps or modules described in connection with the above text and corresponding figures may be performed by hardware and / or software . if the process is performed by software , the software may reside in software memory ( not shown ) in a suitable electronic processing component or system such as a microprocessor , personal computer , mobile electronic device , or a stereo or surround sound system . the software in software memory may include an ordered listing of executable instructions for implementing logical functions ( that is , “ logic ” that may be implemented either in digital form such as digital circuitry or source code ), and may selectively be embodied in any computer readable media for use by or in connection with an instruction execution system , apparatus , or device , such as a computer - based system , processor - containing system , or other system that may selectively fetch the instructions from the instruction execution system , apparatus , or device and execute the instructions . in the context of this disclosure , a “ computer - readable medium ” is any tangible non - transitory means that may contain , store or communicate the program for use by or in connection with the instruction execution system , apparatus , or device . the computer readable medium may selectively be , for example , but is not limited to , an electronic , magnetic , optical , electromagnetic , infrared , or semiconductor system , apparatus or device . more specific examples , but nonetheless a non - exhaustive list , of computer - readable media would include the following : a portable computer diskette ( magnetic ), a ram ( electronic ), a read - only memory “ rom ” ( electronic ), an erasable programmable read - only memory ( eprom or flash memory ) ( electronic ) and a portable compact disc read - only memory “ cdrom ” ( optical ). note that the computer - readable medium may even be paper or another suitable medium upon which the program is printed and captured from and then compiled , interpreted or otherwise processed in a suitable manner if necessary , and then stored in a computer memory . while various embodiments of the invention have been described , it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention . accordingly , the invention is not to be restricted except in light of the attached claims and their equivalents .