SPECTRA OF PERIODIC DIGITAL SIGNALS

hippoの体験会に参加して、気付いた事は、日本人同士でも、充分、外語の練習が出来る事です。

皆で、CDで聞いた言葉を、真似る事が殆どですから...

繰り返し言ってみる事が大事みたいです。

某大学病院の某科では、診療時の会話、症例検討会は、英語だけ使うそうです...(私はドクターでも、ありませんし、大学とも関係ない）

　

「習うより慣れろ」ですね。

　

私も、早速、真似事を...

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著書の引用はアポストロフィ ' で囲ってます。それが、殆どやけども...

　

from ' INTRODUCTORY DIGITAL SIGNAL PROCESSING Paul A.Lynn Wolfgang Fuerst ' p.67-71

　

'A periodic digital signal can be represented by a Fourier Series'

example 1.

MATH a periodic signal

'The coefficients of its line spcetrum indicate the 'amount' of various frequencies contained in the signal.'

$\vspace{1pt}$ Definition of DiscreteFourier Series

in this case,

$a_{k}$ = kth spectral component

is a vector.

because of $x_{k},\qquad$ k starts with one ,so I changed former difinition.

$\qquad$ Why different from the answer?

error: is not correct , is right.

$\vspace{1pt}$

inspection

'if x[n] is a real function of n, the values display a 'mirror-image' pattern

real parts of a $_{1}$ and a $_{6}$ are equal,so are the those of \{a} $_{2}$ and a $_{5}$ .

The imaginary parts shows a similar pattern,but with a change of sign.

This always happens when x[n] is a real function of n.'

successive seven coefficients are...

'identical to the set of $a_{0}$ to $a_{6}$

repetitive ,periodic sequence.'

$\qquad \$

example 2.

Problem 1.Find its Fourier Series coefficients $a_{k}$

......this needs 8 points for sampling, right?

...this needs 4 points,right?

So, I need 8 samples for x[n] to be periodic, right?

$\qquad$

Let's try this.

MATH

(This difinition of x $_{n}$ is good, because I can define $x_{0}$ and others appropriately)

OK ,PASSED

PASSED

But , about $a_{k}$ ,where is a periodicity?...

Paul/Wolfgang wrote

'x[n] has eight samples per period,so its Fourier Series must repeat every eight harmonics.

Our analysis gives only five finite terms,therefore the other three must be zero.'

Let's caluculate other coefficients of x[n].

　

it's OK,but are non-zero!

Real parts of equal zero.

These iimaginary parts are almost equal to zero(.......OK, d'accord

conclusion

　

The series { $a_{k}$ } is really periodic?

　

OK

$\vspace{1pt}$

June 24 2003

$\vspace{1pt}$

This document created by Scientific Notebook 4.1. この文書は次の製品で作成しました Scientific Notebook 4.1.