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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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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 ...
Sammy Apsel's user avatar
1 vote
1 answer

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 ...
Sammy Apsel's user avatar
2 votes
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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 ...
Dan Boschen's user avatar
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Radix2 fft - zero padding output size

With zeros padding the FFT radix2 has different input size than output. How to deal with that? I see two solutions but not sure which one is better/appropriate. Maybe you know some other and better ...
pajczur's user avatar
  • 359
11 votes
4 answers

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? ...
Television's user avatar