# Questions tagged [parsevals-identity]

This tag is for questions regarding Parseval's Identity, an important result in the study of Fourier Series.

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### How to verify Parseval's theorem

I'm wondering how to verify the Parseval's theorem $$\int_{-\infty}^{\infty} f(x)g(x)dx = \int_{-\infty}^{\infty} F(k) G^{*}(k)dk$$ for 2 functions $f(x)$ and $g(x)$ I know how to find the Fourier ...
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### Parseval's Identity Application

In this video, it is stated that Parseval's Identity "is how we go from discrete to continuous." However, I have not been able to find any material that expands on this use of Parseval's ...
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### Generalize Power spectrum density to higher orders

If the power spectrum density for a given time series is given by : $PSD(f) = \frac{2 \Delta}{N} \sum_{j=1}^{N} \delta B^{2}(t_{j}, f)$, where, where $δB(t_{j} , f)$ is the magnitude of the trace ...
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### Factoring inequalities using Iverson identity - confused by double summations in Concrete Mathematics book

In chapter 2 section 4 (multiple sums) of Concrete Mathematics(Graham,Knuth,Patashnik) the authors use Iverson Identity to rearrange the variables' bounds. In particular, they start off with a ...
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