15 votes
Accepted

Why would one use a Hann or Bartlett window?

In reviewing fred harris' Figures of Merit for various windows (Table 1 in this link) the Hamming is compared to the Hanning (Hann) at various values of $\alpha$ and from that it is clear that the ...
Dan Boschen's user avatar
  • 51.3k
13 votes
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Proof that the rectangular window has the best resolution

Wikipedia has a very nice article on window functions https://en.wikipedia.org/wiki/Window_function The basic trade-offs in windows is main lobe width vs side lobe height and overall attenuation. The ...
Hilmar's user avatar
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12 votes

FFT with asymmetric windowing?

I'll use the shorthand window for "window function". With audio, any processing that creates something akin to pre-ringing or pre-echo will sound sloshy like a low bit-rate mp3. This happens when ...
Olli Niemitalo's user avatar
10 votes
Accepted

Is spectral leakage due to windowing 'different' for the DTFT and DFT?

The concept of spectral leakage is not dependent on the context, and it's the same thing for the DTFT as it is for the DFT. It's probably helpful to remember that the DFT of a finite length sequence ...
Matt L.'s user avatar
  • 90k
9 votes
Accepted

Why is each window/frame overlapping?

Why is each window/frame overlapping? Windowing is a means to stationarize signals. Inside a small enough window, you can expect that the properties of the signal chunk do not vary too fast. And you ...
Laurent Duval's user avatar
9 votes

Does windowing affect Parseval's theorem?

Parseval's theorem will hold, but take into account that your signal in the time domain will no longer be $x[n]$. Namely, if you have that $$\sum_{n=0}^{N-1} \Big| x[n] \Big|^2 = \frac{1}{N} \sum_{...
Tendero's user avatar
  • 5,020
8 votes

How to do continuous signal processing (i.e without windowing)?

Yes, it's possible to analyse sound the way ears do. For example, you could compute the DFT of a signal continuously using several Goertzel filters. $$ y_k[n] = e^{j2\pi k/N} y_k[n-1] + x[n] $$ ...
Peter K.'s user avatar
  • 25.7k
8 votes
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Effect of windowing on noise

UPDATE: My previous response did not answer the OP's question. The following addresses the question directly: Bottom line: Prior to windowing in time, each sample in frequency is an IID Gaussian ...
Dan Boschen's user avatar
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8 votes
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What is the difference of windowing functions for FIR filtering?

So, from the discussion in the comments it's clear you know most you need to know. The window method for FIR filter design is based on this idea: We know the "ideal" frequency response $H(f)$ we ...
Marcus Müller's user avatar
8 votes
Accepted

Why doesnt DFT Padding cause sinc like features

The OP is showing very good insight in all the comments stated. A product in the time domain with a rectangular pulse is convolution in the frequency domain with a Sinc. In fact zero padding in time ...
Dan Boschen's user avatar
  • 51.3k
7 votes

Why is each window/frame overlapping?

More overlap means you end up with more windows (of a given length) per second of audio. More windows (of a given length) requires more FFTs which requires more MACs or FLOPs which generally requires ...
hotpaw2's user avatar
  • 35.3k
7 votes

Kaiser window approximation

just implement the Modified Bessel function. it's easy. i always like my window definitions centered about zero, since pretty much all of them are even symmetry. i'll do this in discrete-time, but ...
robert bristow-johnson's user avatar
7 votes
Accepted

Are there windows that create asymmetric sidelobes

The Fourier Transform of any real function of time, has Hermitian symmetry in the frequency domain. The magnitude is even symmetry and the phase is odd symmetry. But you could define a main lobe with ...
robert bristow-johnson's user avatar
7 votes

How Best to Characterise a Window Function

An oldie but a goodie it fred harris's "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform". It has a nice table showing different figures of merit for different ...
Peter K.'s user avatar
  • 25.7k
6 votes

Is the discrete Gaussian kernel an eigenfunction of the DFT?

This answer complements @CedronDawg's answer which introduced this family of eigenvectors. More specifically, this answer presents three algorithms and a hybrid algorithm for generating for a given ...
Olli Niemitalo's user avatar
6 votes

Is the discrete Gaussian kernel an eigenfunction of the DFT?

I have made a tremendous amount of progress on this issue in the last few weeks. The Zeroing Sine Family of Window Functions I have discovered a previously unrecognized class of window functions. ...
Cedron Dawg's user avatar
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6 votes
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Is it customary to correct for the gain of a window?

Yes, it is customary to correct for the gain of a window, except for some cases I refer to later. (If you are interested only in the relative amplitude, of course you do not need to correct for the ...
J-Matthew's user avatar
6 votes

Kaiser window approximation

You could try the exponential window: $$w_n=\frac{ \exp \left[\alpha \sqrt{1-\left(\frac{n-M}{M}\right)^2}\right]}{\exp(\alpha)}$$ $$\alpha=-427.5*10^{-6} A_s^2+0.1808*A_s-3.516$$ or the hyperbolic ...
a concerned citizen's user avatar
6 votes

Window period(overlap) and FFT

In addition to what others have already said, I'll try to answer it from a purely practical point of view (this is also a variant of the overlap-add technique). If your FFT length is 2048, then an ...
dsp_user's user avatar
  • 921
6 votes

How does the effect of windowing change with the phase of the input signal?

What's going on? I think the main issue is the use of detrend='constant' in the calls to signal.periodogram. If I change that to ...
Jason C's user avatar
  • 256
5 votes
Accepted

Extract Sine Phase and Amplitude - accurate and robust method

Regarding your Edit #2: It is not true that phase estimation requires that frequency be at a bin center. However if a frequency estimate requires interpolation between FFT result bins, so does any ...
hotpaw2's user avatar
  • 35.3k
5 votes

How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Knowing the energies of $x_1$ and $x_2$ is not sufficient for determining the energy of $x_3=x_1x_2$. What you can do is determine an upper bound for the energy of $x_3$ given the energies of $x_1$ ...
Matt L.'s user avatar
  • 90k
5 votes

How to calculate resolution of DFT with Hamming/Hann window?

The frequency resolution of a DFT is indeed significantly affected by the choice of window. Two key parameters to consider when selecting a window are the frequency resolution and dynamic range. The ...
Dan Boschen's user avatar
  • 51.3k
5 votes
Accepted

Zero padding - High amplitude

I'd like to apply zero padding to it, for better frequency bin resolution. First of all, let's state it one more time that zero padding does not improve frequency resolution of DFT. It'll only ...
Fat32's user avatar
  • 28.2k
5 votes

Does windowing affect Parseval's theorem?

While the Fourier transform, discrete or continuous, can be regarded as unitary transform i.e a naturally norm preserving change between orthonormal bases in a normed complex vector space, the ...
Jazzmaniac's user avatar
  • 4,584
5 votes
Accepted

Seven term Blackman Harris window

In this document you can find the coefficients of a seven-term Blackman Harris window. Ignoring the bizarre notation, it seems like the window is defined by $$w[n]=\sum_{k=0}^6a_k\cos\left(\frac{2\pi ...
Matt L.'s user avatar
  • 90k
5 votes

Is the DCT prone to spectral leakage like the DFT?

A window function other than rectangular can be applied to suppress sidelobes also with the discrete cosine transform (DCT). Window functions are also sometimes used together with some flavors of DCT ...
Olli Niemitalo's user avatar
4 votes

Choosing the right overlap for a window function

I tried my best but I couldn't find a resource that would list the "good" overlap factors for common and less common windows. Here's a list of window functions and overlap factors that have constant ...
endolith's user avatar
  • 15.8k
4 votes
Accepted

DFT and periodicity

As you have correctly observed, $2N/W$ must be an integer, because the window can only have an integer number of samples. Furthermore, regardless of the upper summation limit, $$Y_k=\sum_{m=0}^Ke^{-j\...
Matt L.'s user avatar
  • 90k

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