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.
7
questions
3
votes
1
answer
127
views
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,...
- 1,983
1
vote
1
answer
131
views
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 ...
- 1,983
1
vote
1
answer
104
views
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 ...
- 113
1
vote
1
answer
83
views
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 ...
- 113
2
votes
0
answers
301
views
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 ...
- 53.8k
1
vote
2
answers
518
views
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 ...
- 359
11
votes
4
answers
4k
views
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?
...
- 457