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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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[...
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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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888 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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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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1answer
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FFT averaging with different block sizes - how to scale the amplitudes

I need to analyze a real-valued time signal with a length of 300000 in the frequency domain. The sampling frequency is 100000Hz. In order to increase the signal-to-noise ratio reduce the "fine-grain" ...
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456 views

Spectral window when FFT is not a power of 2

I am trying to better understand zero padding and the FFT. To do so, I am attempting to plot the spectrum of the Hann window function, i.e. $$ w(n) = \frac{1}{2}\left(1-\cos\left(\frac{2\pi (n+1/2)}{...
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1answer
370 views

Is information lost due to Hanning window perturbations?

I apologize for the obscure phrasing of the title of the post...My question is quite simple... Let us imagine an audio signal (any song will do). We want to apply the Short Time Fourier Transform ...
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1answer
727 views

Adjustment of window length with sliding/moving RMS method for frequency drifts

I'm using a sliding RMS mechanism to compute RMS of a signal, i.e. with a window size of N, I add the squared value of the new sample $x[n]$ to the running total while deducting the squared value of ...
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2answers
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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 ...
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1answer
513 views

Filter, window function and audio signal: how to link them to each other?

I have a question about the implementation of digital filters in CoreAudio. I'm in big trouble because it is a few weeks I'm trying to understand how to implement them. The basic idea is this: while I ...
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175 views

What happens if you apply window after filtering a discrete signal to get it back to its original length?

What happens if you filter a discrete bandpass signal of length $N$ with a bandpass filter(Hann truncated sinc) of length $L$ and apply a window of length $N$ to the filtered signal of length $N+L-1$ ...
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1answer
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What is the purpose of a window function?

I've read that a window function is a mathematical function that is zero-valued outside of some chosen interval. Can someone please explain what this really means?
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Applying a window function to a speech signal

I'm currently developing a speaker recognition system. I have two main problems: What is the most suitable windowing function to apply to a speech signal prior to the STFT? Is it necessary to apply ...
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Why is each window/frame overlapping?

I am currently reading up on some speech recognition theory. As it speech signals usually are non stationary, but if a speech is seen in a very small time frame can it be deemed stationary, as would ...
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0answers
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Where can I find more information about this formula relating a window's time and frequency size?

I remember having seen a formula of the form $C=\frac{B}{L}$ that relates a duration $L$(s) of a window to its width $C$(Hz) in the spectrum (defined at -3dB or so). The constant $B$ would be ...
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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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1answer
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Scaling for a 2D Hanning Window

I am trying to find the PSD of a 2D set of data and representing it as a function of frequency in both these directions. I start with a 2D FFT and generate the 2D hanning window for a $M\times N$ ...
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2answers
391 views

“Don't window a transient signal”

I'm a SP student and still a beginner in the field. When we were learning about window functions, my professor said "you're gonna almost always want to window your data but don't window a transient ...
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1answer
268 views

How to fit Welch's window segments to a time series of variable length

I'm trying to write a small Welch's PSD method in R right now, but I've had trouble finding information on how exactly the window segments are fitted to a given time series. For instance, when the ...
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1answer
1k views

The Fourier transform of a triangular window function

Windowing functions are explained on Wikipedia and they include plots of the Fourier transform for several windowing functions. For the triangle window they provide The above Fourier transform plot ...
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560 views

Effect of window function on audio output

If I have a low pass filter, does the choice of window function I use have any effect on the quality of the audio input? What would be the effective difference between using a rectangular window and a ...
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1answer
206 views

Why do we not use square filters without windows? [duplicate]

This question may sound like "why do we use window functions", but it's not. So here it's: What we currently do: If we have a function $g(t)$ and its Fourier transform $G(f)$, and a window $W(f)$ and ...
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Overlapping power-of-cosine windows with constant weight

I would like to refer you to a relevant question I posed on the Math StackExchange: A generalisation of the Pythagorean trigonometric identity. As can be seen from the question and the answer, what ...
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1answer
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Why does my plot of the Blackman window not match everyone else's in literature?

I've seen the plot for Blackman window as so in a bunch of books, as on this website: But plotting the same equation on Wolfram Alpha yields a different plot: Why is their graph not centered around ...
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2answers
702 views

What is the meaning of half window functions?

In fig. 4 on p. 4 of the paper Extracting the frequencies of the pinna spectral notches in measured head related impulse responses (J. Acoust. Soc. Am. 118, 2005 ), a half Hann window is used (Hann ...
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275 views

Beginner's question on LPF, Need for Sinc and windowing [duplicate]

As a student who has never constructed any real world DSP application, I am inclined to ask the following. Convolution in time domain is multiplication in frequency domain. For low pass filtering, ...
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2answers
132 views

How do you model a rolling shutter in the frequency domain

Say you have an image in time domain: $$a(x, y, t)$$ The Fourier transform is then: $$A(k_x, k_y, f)$$ So far so good. What if we now introduce a rolling shutter. How would one model that. I'd ...
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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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1answer
49 views

What does the 'B' parameter represent in Wikipedia's page on window functions?

I was trying to learn some more window functions and was referencing the Wikipedia article on the subject. I've noticed on a lot of the plots, there appears to be a capitalized and italicized letter B....
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3answers
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Librosa stft + istft - Understanding my output (which always seems too perfect) at varying window lengths

I've just started to use Python with Librosa for a DSP project I'll be working on. First thing I've been trying to do is determine my preferred parameters for the FFT window size, and hop-distance. ...
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1answer
151 views

Question regarding estimation of signal tone parameters (frequency, amplitude, and phase) using Macleods algorithm

I plan to use Macleods algorithm in order to estimate the parameters (frequency, amplitude, and phase) of one or more sinusoids from a block of N uniformly spaced ...
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1answer
563 views

Modified Tukey window applied in frequency domain

In analysis of transient signals (ground motion time-series) in seismology, many operations are performed in frequency domain and it is common practice to apply a filter which is like a modified Tukey ...
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444 views

Windowing before viewing a filter frequency response?

It is well known that it is a good idea to apply windowing to a signal, before obtaining its DFT and viewing its frequency response. But is it a good idea to apply windowing to the impulse response ...
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551 views

How to prove main-lobe side-lobe ratio in hann window is $-32\textrm{ dB}$?

I found that the value of the main lobe is about $N$, when I try to calculate the value of the sidelobe I got $0$, I assumed that the peak is at $\theta=\frac{6\pi}{N}$. How can I find the size of ...
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1answer
85 views

DFT and periodicity

My problem is related to the periodicity of DFT. Having the following expression $$ Y_{k}=\sum_{n=0}^{2N-1}e^{-j\frac{2\pi mk}{2N}} $$ I can easly find that the upper function is $2N$ periodic. So ...
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1answer
551 views

MRI reconstruction using windowing based apodization

I am trying to apply windowing to do MRI reconstruction. I have a 256 point one dimensional k-space samples which look as follows: Here, the real part(green) is flat around 0 and the blue curve is ...
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1answer
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How is the energy of $x_1\cdot x_2$ related to the energies of $x_1$ and $x_2$?

Let's say first signal x1 = [1 2 3 4], second signal x2 = [0.08 0.77 0.77 0.08] (Hamming window), third signal ...
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1answer
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How to do continuous signal processing (i.e without windowing)?

I'm working in speech recognition research, and I wonder if there is a way to analyse sound just like how ears do (i.e. without windowing), so for example to take some feature continuously with an ...
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2answers
203 views

Reduce “flicker” in spectrum analysis / spectrogram

I'm performing a series of FFTs on windowed extracts of an input signal, to get a frequency spectrum over time. This is for a visualisation - I'd like to keep the window small, so the visualisation ...
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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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1answer
59 views

extending windowing function to higher dimensions

I was looking at this particular thread that discusses extending windowing functions for singling function to higher dimension. There is one bit in the accepted answer that I could not get my head ...
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0answers
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Window function on large arays

Hello I'm reading the following document to better understand windowing and how to use it. "Spectrum and spectral density estimation by the Discrete Fourier transform (DFT), including a ...
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Specifications (N) FIR Low Pass Resamplig, Hamming Window

I'm learning about DSP and I've doubts. The resampling process can be do it with only one filter. $L$: Increment Sample Rate Integer $M$: Decrement Sample Rate Integer $f_S$: Frequency Sampling ...
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1answer
238 views

Shape of Kaiser windowing function FFT response

I'm trying to determine the shape of the FFT response of a signal which had a kaiser windowing function applied to it. What I mean by this is if the shape is a normal bell curve or a Lorentzian ...
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1answer
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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 ...
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1answer
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DFT normalization for amplitude estimation

After an interesting recent answer, I'm doing some research on proper DFT normalization for sinusoidal peak estimation. It's clear that to get the correct amplitude from DFT peaks we need to normalize ...
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1answer
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What is the range for alpha in window equations

Alpha is used in many window functions e.g. What is the range that alpha can take and is it the same across all uses of alpha in the equations? e.g. Will any alpha still result in a stable result, e....
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2answers
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Window functions and indexes larger than N/2

How does the n index for a window with $0 \le |n| \le N/2$ e.g the Bohman window function, get implemented when having a specific window size? ...
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1answer
135 views

Fixing for windowing function in FFT

I've been learning about the FFT and about the usefulness of windowing functions. A problem I'm running into is the affect of windowing functions on the amplitude of signals in the FFT. For example, ...
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4answers
866 views

Windowing function squared?

Reading this paper about WSOLA (Verhelst, Roelands) (PDF) At page 2 there's a "time-warped STFT's synthesis function" involving $v(n)=w^2(n)$ which is a windowing function. A windowing function ...