Hey Matt, Thanks for a reply. I guess I was getting a little too excited. I admit signal transforms are typically numerical in nature, but there are many problems in digital signal processing (DSP) that can be converted into algebraic problems over Laurent and polynomial rings and are generally easy to solve with current methods of symbolic computation. Most Real and complex-valued data satisfy the mathematical properties of a field. I am mostly concentrated on using the method of Gröbner bases as the computational tool.
Besides this, there is also a whole different category of symbolic signals, which do not rely on any mathematical structure. Symbolic signals differ from numeric signals in that symbolic sets have no additional mathematical structure. A set of symbols is not a field because algebraic operations on symbols are usually not meaningful. For example, addition, multiplication, and numeric ordering cannot be performed on symbols.Although this is a second part is optional for my project. I am mostly focused on symbolic computation and signal processing. Please let me know what you think about it. References: 1. http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=809533 2. http://en.wikipedia.org/wiki/Gr%C3%B6bner_basis 3. http://en.wikipedia.org/wiki/Polynomial_ring On Sun, Feb 23, 2014 at 11:02 PM, Matthew Rocklin <[email protected]>wrote: > Hi Saket, > > Thanks for reaching out. Sorry for not getting back to you the first > time; we're all a little busy. > > I personally find signals processing transforms to be very interesting. I > usually think about these from a numerical perspective though, not a > symbolic one. Maybe you can describe how signals processing would fit into > the rest of SymPy and the symbolic computing world. > > -Matt > > > > > On Sun, Feb 23, 2014 at 9:13 AM, Saket Dewangan <[email protected]>wrote: > >> I was wondering if anyone liked the idea or not. I would be really glad >> if Aaron or anyone else would have a say in this. >> >> Thank you. >> >> >> On Fri, Feb 21, 2014 at 8:15 PM, Saket Dewangan <[email protected]>wrote: >> >>> Hi, >>> I am a pre-final year student at IIT Delhi, majoring in Electrical >>> Engineering with a minor in Mathematics and Computing Applications. I have >>> a huge motivation in computer algebra. I have a vast experience with Python >>> and I have also used SymPy before for applications in Neural Networks. I am >>> interested in Google SoC and would be really happy to code under SymPy's >>> banner. >>> >>> I wanted to implement different transforms techniques (FFT, Circular >>> DFT, IDFT, Discrete Cosine Transform etc) for my project. I know laplace >>> is there in SymPy already, and I sure hope so for Fourier and even >>> z-transform, but I am not so sure about others. Do tell me if this idea >>> sounds any good. >>> http://en.wikipedia.org/wiki/Fast_Fourier_transform >>> >>> http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Circular_convolution_theorem_and_cross-correlation_theorem >>> >>> http://en.wikipedia.org/wiki/Discrete_Fourier_transform#Expressing_the_inverse_DFT_in_terms_of_the_DFT >>> http://en.wikipedia.org/wiki/Discrete_cosine_transform >>> >>> In the listed projects ( at >>> https://github.com/sympy/sympy/wiki/GSoC-2014-Ideas), following >>> projects (in the order of preference) struck me out the most: >>> 1. Series expansions >>> 2. ODEs >>> 3. Group Theory >>> 4. Polynomials module (Univariate) >>> >>> >>> Expecting a positive response. >>> Thank you. >>> >>> PS- I tried posting once before, I do't know if that got posted. Pardon >>> for a re-post. >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "sympy" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at http://groups.google.com/group/sympy. >>> For more options, visit https://groups.google.com/groups/opt_out. >>> >> >> >> >> -- >> ------------------------------------------------------ >> Saket Dewangan, >> Third Year Undergraduate Student, >> Electrical Engineering Department, >> IIT Delhi. >> Ph- 8860715533 >> e-mail: [email protected] >> ------------------------------------------------------- >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > -- ------------------------------------------------------ Saket Dewangan, Third Year Undergraduate Student, Electrical Engineering Department, IIT Delhi. Ph- 8860715533 e-mail: [email protected] ------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAMp1gYPCLS2r%2B6dttY91tRqBSbibGiRGtHqz0MFnYMdYe9GCRw%40mail.gmail.com. For more options, visit https://groups.google.com/groups/opt_out.
