"John Corbett" <corbett@[EMAIL PROTECTED]
> wrote in message
news:corbett-2705081343560001@[EMAIL PROTECTED]
> In article
> <A_ydnTyHF4nC1KnVnZ2dnUVZ_gmdnZ2d@[EMAIL PROTECTED]
>, "Arny
> Krueger" <arnyk@[EMAIL PROTECTED]
> wrote:
>
>> "John Corbett" <corbett@[EMAIL PROTECTED]
> wrote in message
>> news:corbett-2105080939570001@[EMAIL PROTECTED]
>>> In article
>>> <S9ydnc_rv_JNT6_VnZ2dnUVZ_iydnZ2d@[EMAIL PROTECTED]
>, "Arny
>>> Krueger" <arnyk@[EMAIL PROTECTED]
> wrote:
>>>
>>
>>>> Lots of even harmonics make waves asymmetrical. All
>>>> even harmonics give you a wave that has either the
>>>> upper or lower side completly cut off.
>
> When I noted that what you claimed was not true, you
> responded:
>
>> I didn't say merely lots, I said "all". By that I mean
>> only even harmoncs, and all even harmonics (including
>> the z*****h) present. IOW all, any way you look at it.
>
> Mr. Krueger, you are still wrong.
>
> A simple counterexample is sufficient to show that a wave
> can have "only even harmoncs, and all even harmonics
> (including the z*****h) present" yet fail to have its
> upper or lower side completely cut off. For example,
> consider a wave with these Fourier coefficients:
>
> a_0 = 1/4 = constant term (DC component)
> a_1 = 1 = fundamental cosine term
> b_1 = 0 = fundamental sine term (not needed)
> a_n = (1/5)^(n/2) if n = 2, 4, 6, ...
> a_n = 0 if n = 3, 5, 7, ...
> b_n = (1/5)^(n/2) if n = 2, 4, 6, ...
> b_n = 0 if n = 3, 5, 7, ...
> and let
> A = sum of cosine terms for n > 1, and
> B = sum of sine terms for n > 1.
>
> It is easy to see that -1/4 <= A <= 1/4 and -1/4 <= B <=
> 1/4 and that -1/2 < A + B < 1/2, so
>
> f(t) = a_0 + a_1 cos( t ) + sum a_n cos( nt) + sum b_n
> sin( nt )
>
> = 1/4 + cos( t ) + A + B
>
> By itself the fundamental cosine term ranges from -1 to 1
> on every cycle, so adding the higher-order terms (the A
> and B stuff) without the constant term would cause the
> maximum to be between 0.5 and 1.5, and the minimum
> between -1.5 and -.5. Now adding the constant term, we
> see that that f(t) reaches a maximum that is at least .75
> and a minimum that is less then -.25, so it does not have
> its top or bottom completely cut off.
You're still reading your own ideas into what I wrote, John.
I didn't say that all combinations of all even harmonics always give a
wave
that has all of either the positive or all of the negative cut off. You
made
most of that up in your endless quest to split yet another hair.
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