# Questions tagged [dirichlet-kernel]

The Dirichlet kernel is the convolution kernel for the Discrete Fourier Transform (DFT) to interpolate between the discrete bins or samples of the DFT or of the inverse DFT.

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### Best Methods for Interpolating Short Non-Periodic Bandlimited Signals

I need advice on interpolating a very short (N < 10) discrete, bandlimited signal that is sampled above the Nyquist rate. I understand that technically finite length signals have infinite bandwidth,...
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### What are the advantages of using the Dirichlet kernel for interpolation?

Suppose we define the Dirichlet kernel as: $$\frac{\sin(\pi N x /2)}{\pi N\sin(x /2)}$$ (Note: I'm not entirely sure what the standard definition of the Dirichlet kernel is; mine is slightly ...
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### Calculating the main lobe width of Dirichlet kernel

The Dirichlet kernel of order $N$ is defined as: $$D(\theta,N)=\frac{\sin(N\theta /2)}{\sin(\theta /2)}$$ We know that the main lobe widths between zero crossings is: $4\pi/N$ I was wondering if ...
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### Multiplying a finite signal with a unity window

I have a simple question to ask: Suppose $x[n]$ is finite and has a support for $|n|<L$ Let's denote its DTFT by $\operatorname{DTFT}\big\{x[n]\big\}(e^{j\omega})=X(\omega)$ Let's consider a unity ...
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### Frequency Interpolation of DFT to create Zero-Padded IFFT

As a response to this question I have proposed interpolating new samples in a DFT (meaning the frequency samples of an existing DFT result) sufficient to be the new samples that if we were to take the ...
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### Whittaker-Shannon ($\mathrm{sinc}$) interpolation for a finite number of samples
Given an infinite number of samples $(N)$, a higher (or lower) number of samples $(cN)$ can be derived using sinc interpolation followed by sampling. How can this be applied to finite length signals? ...