python - Fourier transform in scipy and Parseval's identity -


while working on fft in python, i'm running problems normalization of function , calculating squared sum of coefficients.

my code follows:

import pandas pd import numpy np import scipy.fftpack   # sample points n = 1024  # sample spacing t = 1.0/512.0  # example function x = np.linspace(0.0, n*t, n) y = 1.5 * np.sin(5*2*np.pi*x) + 3 * np.sin(6*2*np.pi*x)  df = pd.dataframe({'x': x, 'y': y})  sumy = sum(abs(df['y'])**2)  df['fft (y)'] = scipy.fftpack.fft(df['y'])/(n/2) df['fft (freq)'] = scipy.fftpack.fftfreq(n, t)  sumffty = sum(abs(df['fft (y)'])**2)  print sumy, sumffty

according parseval's identity, sums should equal; however, they're off factor of 256 (sumffty being smaller one). missing?

parseval's theorem states total power in 2 domains (space/time , frequency) equal. statement, dft this. notice, in spite of 1/n on right, not mean power, total power. reason 1/n normalization convention dft.

put in python, means time/space signal sig, parseval equivalence may stated as:

np.sum(np.abs(sig)**2) == np.sum(np.abs(np.fft.fft(sig))**2)/sig.size

below complete example, starting toy cases (one , 2 dimensional arrays filled 1 1s). note used .size property of numpy.ndarray, returns total number of elements in array. hope helps!

import numpy np  # 1-d, 4 elements: ones_1d = np.array([1.,1.,1.,1.]) ones_1d_f = np.fft.fft(ones_1d)  # compute total power in space , frequency domains: space_power_1d = np.sum(np.abs(ones_1d)**2) freq_power_1d = np.sum(np.abs(ones_1d_f)**2)/ones_1d.size print 'space_power_1d = %f'%space_power_1d print 'freq_power_1d = %f'%freq_power_1d

i'm sorry couldn't use example directly--i'm not pandas user , couldn't understand perfectly.


Comments

Post a Comment

Popular posts from this blog

powershell Start-Process exit code -1073741502 when used with Credential from a windows service environment -

i'm running strange behavior powershell start-process call. here call: $process = start-process ` "c:\somepath\mybinary.exe" ` -passthru ` -credential $defaultcredential ` -wait ` -workingdirectory "c:\somepath" ` -loaduserprofile if ($process.exitcode -ne 0) { #do } this call return exit code - 1073741502 . after quick search, exit code seems related generic error when program not load required dll (aka. status_dll_init_failed ). when run without -credential $credential program runs correctly. in order isolate problem, manually launched some.exe in prompt target credential , runs smoothly. so problem seems come way start-process cmdlet launch process. i found potential solutions problem tried apply no luck : link , link . would have idea of what's going on here ? edit 1: run proc mon monitoring program activities when launched directly or via powershell script. problem seems occur when loading kernelbase
Read more

twig - Using Twigbridge in a Laravel 5.1 Package -

i'm trying create laravel 5.1 package uses twigbridge instead of .php views. can normal .php views display fine, when try make use of .twig templates i'm met error. possible use twigbridge templates when creating views laravel package or pretty stuck blade , php ? edit 1: loading twig template without extending works. it's when start using {% extends 'file' %} error comes out. i error error loading /virtual/laravel/packages/username/mypackage/src/views/sample.twig: template "templates.master" not defined () in "/virtual/laravel/packages/username/mypackage/src/views/sample.twig" @ line 1. my folders username |_ mypackage |_ src |_ controllers - samplecontroller.php |_ views |_ templates - master.twig - sample.twig twig template sample.twig {% extends 'templates.master' %} {% block content %} {{ parent()
Read more

c# - LINQ join Entities from HashSet's, Join vs Dictionary vs HashSet performance -

i have hashset's each stores t, have written test application compares different relation algorithms can think of, i'm not pleased results getting. does there exist more efficient ways of achieving object relations, once testing? using system; using system.collections.generic; using system.linq; using system.text; using system.threading.tasks; using system.diagnostics; namespace linqtests { class program { static void main(string[] args) { hashset<user> usertable = new hashset<user>(); hashset<userproperty> userpropertytable = new hashset<userproperty>(); #region lets create dummy data. console.writeline("please wait while creating dummy data, can take while..."); console.writeline(""); int rows = 1000000; for(int x = 0; x < rows; x++) { random rnd = new random(); // ad
Read more