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Why the exponent must be a negative in the Fourier transform of any sequence? What happens with expressions

$$x(m)=\dfrac{1}{2\pi}\int_{-\pi}^{\pi}X(w)\exp(jmw)dw$$ if we define the Fourier transform of sequences as:

$$X(w)=\sum_{-\infty}^{\infty}x(m)\exp(jmw)$$ tal que $-\pi\leq w \leq \pi.$

recall that Fourier Transfrom of sequence $x(n)$ is $X(w)=\sum_{-\infty}^{\infty}x(n)\exp(-jnw)$

I am found that $x(m) = x(-m)$ this is true?

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    You seem to have confused Fourier transforms with Fourier series.2012-11-13
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    Why? I'am talking about sequences ...2012-11-13
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    So $X$ is a sequence, and $\int_{-\infty}^{\infty}$ is really $\sum_{-\infty}^{\infty}$?2012-11-13
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    sorry integral limits are $\int_{-\pi}^{\pi}$2012-11-13
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    Ah, then in English, we call this expression the "Fourier series" for $X$. While it is related to the Fourier transform, it is usually denoted "Fourier series" to make it a distinct concept.2012-11-13
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    I'm extract these definitions of book Anil K. Jain. where say Fourier Transform of Sequences (Fourier Series).2012-11-13
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    Ah, the problem is you start with $X$ and define the sequence $x(m)$, which is then used to define $X$, which seemed confusing to me.2012-11-13

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