Questions tagged [window-functions]

In signal processing, a window function is a mathematical function that is zero-valued outside of some chosen interval.

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3answers
13k views

What should be considered when selecting a windowing function when smoothing a time series?

If one wants to smooth a time series using a window function such as Hanning, Hamming, Blackman etc., what are the considerations for favouring any one window over another?
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2answers
3k views

Why would one use a Hann or Bartlett window?

Suppose we're designing a low-pass FIR filter, and I want to use one of these three windows: Bartlett, Hann or Hamming. From Oppenheim & Schafer's Discrete-Time Signal Processing, 2nd Ed, p. 471:} ...
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2answers
819 views

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

I'm currently trying to improve my foundational understanding of spectral leakage due to windowing. The more I have been reading about it, the more I'm starting to think that 'windowing spectral ...
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3answers
4k views

FFT with asymmetric windowing?

Common non-rectangular window functions all seem to be symmetric. Is there ever a case when one would want to use a non-symmetric window function before an FFT? (Say if the data on one side of the ...
4
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4answers
11k views

Choosing the right overlap for a window function

On Wikipedia there is quite a list of window functions. However, when you are doing a lot of STFTs, you often have to have some overlap to get better results. Generally an overlap factor of 2 (i.e., ...
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2answers
63k views

How to apply Hamming Window?

I am new in matlab and signal processing. The time series that have been used are obtained from accelerometer in a building. As far as I understand both the time series' length and window function ...
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2answers
242 views

Where do we use windowing?

I have been studying about the box window and am unable to understand one thing, do we first sample a signal and then window it resulting in up-scaling or downscaling, or is windowing a practical case ...
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2answers
535 views

Kaiser window approximation

Are there any "good" low-computational-cost approximations for parameterized Kaiser window generation suitable for small systems/languages that do not include Bessel functions in their standard ...
3
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1answer
2k views

What is the relation of the transition band's width and the filter order for the FIR windowing method

When designing an FIR filter using the windowing method, how can one estimate the filter order ? It's obvious that the type of window and the transitions band's width has some effect on the order.
2
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3answers
525 views

What is the relation between windowing and hopping in audio DSP

While using short-time Fourier transform (STFT), it is common to use window function, usually tapered. Will this not alter the original signal $x[n]$ and the STFT may no more be the true STFT of $x[...
5
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1answer
21k views

Why should one use windowing functions for FFT?

So I just revised my pitch calculation algorithm using a harmonic product spectrum algorithm. I was just curious about why this explanation of Harmonic Product Spectrum states that you need to ...
7
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2answers
939 views

Why are there so many windowing functions?

Many windowing functions are listed here in the Mathematica documentation. I tried using a few to reduce leakage when computing a Discrete Fourier Transform. From what I could tell it made little ...
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2answers
2k views

Effect of windowing on noise

I understand that truncating a signal in time 'smears' the frequency response depending on the window chosen. In general, the shorter the signal duration, the more 'flattened' the frequency response, ...
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2answers
20k views

How do I apply a function window to a signal?

How can I apply a window function like Hamming or Lanczos to a signal, using its coefficients? I mean, which method can I use to do this? FFT? Convolution? Which method has the better performance?
4
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1answer
8k views

STFT: why overlapping the window?

For STFT, we impose window of certain size onto the original signal, then we perform fft on each window. The uncertanty about frequency and time is determined by the width of the window, however, I ...
6
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3answers
7k views

RMS calculation in frequency domain after windowing

I can calculate RMS in frequency domain as derived from Parseval's Theorem. But what if I have applied a windowing function before doing the FFT (in my case a Hann window)?. Now the RMS values are ...
4
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1answer
46 views

Amplitude Estimating Using a Windowed DFT

Let's say we want to estimate the amplitude A of a mono-frequent signal using a windowed DFT. The frequency of the signal is unknown, and the frequency resolution of the DFT is limited, thus it cannot ...
2
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4answers
2k views

Intuitively, why is windowing function a low-pass filter?

I'm trying to intuitively understand why a windowing function of a signal is a low-pass filter. I know its DTFT is a sinc function, making it mathematically a low-pass filter, but my logic says ...
2
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3answers
1k views

best window for close frequency components

I'm currently designing a receiver which has to determine whether a signal contains specific frequencies or not. The frequencies are at constant 215Hz difference: ...
2
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1answer
568 views

Optimal window function for amplitude estimation?

Assume you want to estimate the amplitude of a known frequency sinusoid in additive Gaussian (white or pink) noise. Also assume mainlobe width/sidelobe decay doesn't matter. Windows should be ...
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3answers
3k views

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

The frequency resolution of a DFT with a rectangular window of size $N$ is given by $f_s/N$. However, when using other window functions like a Hamming or Hanning window the resolution gets worse. How ...
0
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1answer
989 views

Power Spectrum in dBFs

I'm trying to get the spectrum of my signal in dBFS units. I'm not sure what is the refernce that I should devide by. I computed the power spectrum as follows: 1) FFT normalized to the number of ...
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2answers
114 views

Conditions for symmetric and unimodal windows in both time and frequency domains

After a lecture on harmonic analysis and time/frequency methods, I reconsidered the Gaussian kernel, defined in continuous time. It is unimodal and symmetric, and its continuous Fourier transform is ...
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2answers
1k views

Fourier transform artifacts

My starting point in what follows is a radially symmetric random field. Taking the Fourier transform of this (and plotting it in logarithm to highlight the patterns), I obtain the following image in ...
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2answers
5k views

Extracting accurate phase and amplitude information from FFT with an arbitrary number of samples

This is a followup question to one I asked earlier based on the chat after the answer given by @hotpaw2, and cross-posted from stackoverflow since it was suggested it is more relevant to DSP. I have a ...
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2answers
908 views

Working around FFT windowing?

I have the following problem, that I ran into recently, when calculating the spectra of data that I obtain from a measurement technique, we are using in our group. In short what we do in the ...
2
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1answer
410 views

PSD scaling due to the windowing

I am struggling with the following problem for a while: If I have signal of duration N and I apply window (assume rectangular window) of size M < N how will this influence PSD of that signal after ...
2
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1answer
1k views

Measure scalloping loss of window function

Is there an easy/general way to calculate this? For instance, the rectangular window has a maximum scalloping loss of 0.3634, which can be derived in frequency domain from a normalized ...
2
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1answer
2k views

Effect of Windowing Function on Autocorrelation Function

I need to compute FFT components and autocorrelation of a discrete signal. When I do not use any window function before taking FFT of the signal I get a reasonable AC function from FFT that includes ...
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1answer
157 views

Modified Periodogram function in MATLAB

Given below is a function written in MATLAB for computing the modified periodogram, taken from Hayes, Statistical Digital Signal Processing and Modeling ...
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0answers
125 views

Lost power while using FFT with apodizing mask

Previously I asked this question about FFT artifacts. The solution that is most easily implemented is using an apodizing mask on the original image, tapering the borders to zero making the image left-...
0
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1answer
225 views

Is there a closed form expression for main-lobe width increase given a window?

We know that when we window a signal, we increase the main-lobe width. Let 'main-lobe-width' here be the null-to-null bandwidth of the main lobe. Let us further more say that the main-lobe width of a ...
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2answers
731 views

Spectral leakage - understanding the integer number of cycles while windowing

I am reading tutorials about windowing and have read following sentence: For an integer number of cycles, all smoothing windows yield the same peak amplitude reading and have excellent amplitude ...