Path: csiph.com!usenet.pasdenom.info!gegeweb.org!de-l.enfer-du-nord.net!feeder2.enfer-du-nord.net!newsfeed.eweka.nl!eweka.nl!feeder3.eweka.nl!newsfeed.xs4all.nl!newsfeed1.news.xs4all.nl!xs4all!newsgate.cistron.nl!newsgate.news.xs4all.nl!post.news.xs4all.nl!not-for-mail
Return-Path: <python-python-list@m.gmane.org>
X-Original-To: python-list@python.org
Delivered-To: python-list@mail.python.org
X-Spam-Status: OK 0.005
X-Spam-Evidence: '*H*': 0.99; '*S*': 0.00; 'tutorial': 0.03; 'answering': 0.09; 'meaningful': 0.09; 'received:80.91': 0.09; 'received:80.91.229': 0.09; 'received:gmane.org': 0.09; 'received:list': 0.09; 'random': 0.14; 'benjamin': 0.16; 'compute': 0.16; 'corresponds': 0.16; 'element:': 0.16; 'numpy': 0.16; 'peak': 0.16; 'received:80.91.229.3': 0.16; 'received:plane.gmane.org': 0.16; 'component': 0.16; 'index': 0.16; 'wrote:': 0.18; 'import': 0.22; 'header:User-Agent:1': 0.23; 'header:X-Complaints-To:1': 0.27; 'header:In-Reply-To:1': 0.27; '>>>>': 0.31; 'operations': 0.35; 'example,': 0.37; 'question,': 0.38; 'to:addr:python-list': 0.38; 'pm,': 0.38; 'to:addr:python.org': 0.39; 'received:org': 0.40; 'duration': 0.60; 'received:173': 0.61; 'maximum': 0.63; 'skip:n 10': 0.64; 'more': 0.64; 'lowest': 0.74; 'square': 0.74; 'wave': 0.74; 'oscar': 0.84; 'received:fios.verizon.net': 0.84
X-Injected-Via-Gmane: http://gmane.org/
To: python-list@python.org
From: Terry Jan Reedy <tjreedy@udel.edu>
Subject: Re: Harmonic distortion of a input signal
Date: Sun, 19 May 2013 19:19:55 -0400
References: <eb271b5d-ee83-4f0e-b8ea-5b129c7cb771@googlegroups.com> <mailman.1846.1368977695.3114.python-list@python.org> <c841061c-2bae-4e41-bac2-f9cd9606c783@googlegroups.com> <CAHVvXxQURRKyxAV12YeqmpkkWj7sPC1Eczma6SJidLSjU6w-=g@mail.gmail.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
X-Gmane-NNTP-Posting-Host: pool-173-75-251-66.phlapa.fios.verizon.net
User-Agent: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:17.0) Gecko/20130509 Thunderbird/17.0.6
In-Reply-To: <CAHVvXxQURRKyxAV12YeqmpkkWj7sPC1Eczma6SJidLSjU6w-=g@mail.gmail.com>
X-BeenThere: python-list@python.org
X-Mailman-Version: 2.1.15
Precedence: list
List-Id: General discussion list for the Python programming language <python-list.python.org>
List-Unsubscribe: <http://mail.python.org/mailman/options/python-list>, <mailto:python-list-request@python.org?subject=unsubscribe>
List-Archive: <http://mail.python.org/pipermail/python-list/>
List-Post: <mailto:python-list@python.org>
List-Help: <mailto:python-list-request@python.org?subject=help>
List-Subscribe: <http://mail.python.org/mailman/listinfo/python-list>, <mailto:python-list-request@python.org?subject=subscribe>
Newsgroups: comp.lang.python
Message-ID: <mailman.1851.1369005609.3114.python-list@python.org>
Lines: 41
NNTP-Posting-Host: 2001:888:2000:d::a6
X-Trace: 1369005609 news.xs4all.nl 15996 [2001:888:2000:d::a6]:47523
X-Complaints-To: abuse@xs4all.nl
Xref: csiph.com comp.lang.python:45572

On 5/19/2013 6:49 PM, Oscar Benjamin wrote:

>>>> import numpy as np
>
> Create a square wave signal:
>
>>>> x = np.zeros(50)
>>>> x[:25] = -1
>>>> x[25:] = +1
>>>> x
> array([-1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,
>         -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,  1.,
>          1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,
>          1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])
>
> Compute the magnitude spectrum:
>
>>>> spect = abs(np.fft.fft(x)[:25])
>>>> spect
> array([  0.        ,  31.85194222,   0.        ,  10.67342282,
>           0.        ,   6.47213595,   0.        ,   4.69726931,
>           0.        ,   3.73254943,   0.        ,   3.13762901,
>           0.        ,   2.7436023 ,   0.        ,   2.47213595,
>           0.        ,   2.28230601,   0.        ,   2.15105461,
>           0.        ,   2.06487174,   0.        ,   2.01589594,   0.        ])
>
> Find the index of the maximum element:
>
>>>> np.argmax(spect)
> 1
>
> So the peak is the lowest non-zero frequency component of the DFT. In
> Hz this corresponds to a frequency of 1/T where T is the duration of
> the signal.

While you were answering a specific question, I think the above is a 
nice tutorial example, because it is more meaningful than arbitrary 
operations applied to random data.