# 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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### How Best to Characterise a Window Function

How do I characterise my window function? Do please forgive me here as I am more a practical than theoretical person. I have invented a window function which I use prior to discrete Fourier transforms....
83 views

### Dropping the zeros at the edge of window functions

I have learned that Scipy's implementation of the Hann window allows receiving both a symmetric window, and a periodic window (meaning the last zero element is dropped). As far as I understand, the ...
1 vote
74 views

### N-point DFT of window function

I am currently choosing a window function to analyze signals in frequency domain. While I understand the reasoning behind using a window function and what to look for concerning main lobe and side ...
23 views

### Kaiser window but desired frequency response extends beyond pi?

Passband : 0 to 0.5π Stopband : 0.7π to 2π Is there a way to reduce this to a 0 to π scale? If I had to guess, we should be able to simply divide the edge frequencies by 2 and use the time scaling ...
1 vote
56 views

### Understanding FIR windows

We learnt about the various windowing techniques recently and I can't seem to wrap my head around why one would use anything other than a rectangular window. I created a signal with 10 evenly spaced ...
223 views

### Amplitude scaling of window functions for FFT

I need to perform an FFT on a signal sampled with 20 kHz and a measurement time of about 10 seconds. The signal contains frequencies of up to 2 kHz but I am mainly interested in the bandwidth of 0 to ...
1 vote
97 views

### Effect of windowing on signals

I have an input signal of frequency 1000Hz. Sampling frequency=16kHz. I compute the FFT on 128 input samples and plot the magnitude spectrum. I am not doing the normalization by 128. My two sided ...
83 views

### Proof for the energy correction factor of DFT

I am looking for a mathematical proof for the energy correction factor in conteext of windowed discrete fourier transform. In Spectrum and spectral density estimation by the Discrete Fourier transform ...
81 views

### How to understand "independent sample rate" of windows?

A window metric called independent sample rate is given in a book that I recently read. It says that in spectral estimation, the variance of power-level estimates is inversely proportional to the ...
1 vote
68 views

### What is the necessity of shifting the impulse response of a filter to the front of the time domain buffer and windowing?

I was reading the answer to this question provided by Phil Karn. In the answer, it has been said: Ensure that the impulse response of your lowpass filter is shifted to the front of your time domain ...
48 views

### Trade offs in window based design of FIR filter

Please find attached snap of proakis dsp book. It shows rectangular window has minimum value of stop band attenunation and transition width and as we go on towards Hamming and Blackman window,stop ...
694 views

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

I am calculating the SNR (signal power to noise power) for a sine wave. I don't have an integer number of periods in the waveform being analyzed, so I am using a flattop window to reduce spectral ...
101 views

### Applying Hanning window $w_n=1-\cos\Big(\frac{2\pi n}{N}\Big)$ to data

I have a time-series data file in python and I am asked to apply a Hanning window $w_n=1-\cos\Big(\frac{2\pi n}{N}\Big), 0\leq n\leq N=\text{file length}$ to the data given. I am very new to this ...
142 views

### FFT of 2 sine tones using windowing and zero padding. Wrong FFT amplitude

Here is my attempt to perform an FFT on a random signal with 2 tones in which I applied zero padding AFTER windowing. (I did not apply zero padding before windowing because that would suggest that the ...
101 views

### Correct Windowing Effect at Amplitude Scale

I am trying verify the noise floor returned by Matlab sinad(). I am able to get the results matching by summing power spectrum density with $\frac{f_\text{s}}{N}$. ...
51 views

### Determining minimum window length for DTFT [duplicate]

Let $x(t) = \cos(2\pi\times15t)+\cos(2\pi\times22t)+\cos(2\pi\times35t)+\cos(2\pi\times42t)$ and $\forall t\in\mathbb{R} :w(t) = 1$. We sample $x(t)$ and $w(t)$ with $F_s = 92 \ \text{Hz}$. So we ...
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### What is the right scaling factor to get the amplitude after aplying a hanning window? [duplicate]

I have a waveform where I sliced the flat top so I can do some analysis on the amplitudes of each frequency. I have a dataset of N measurements each with M samples of current (A) over time (...
135 views

### Are there windows that create asymmetric sidelobes

I am working on a project which uses radar imaging. The radar imaging takes place at a relatively small distance from the radar (0.25m to 3m). The data is collected using an FMCW radar. The FFT of the ...
1 vote
273 views

### Converting a triangle from the frequency domain to the time domain

I’ve been given a triangular signal that looks like this: $$X^{F}(\omega) = (2 -|\omega|) \cdot W_{[-2,2]}(\omega)$$ (this is just my interpretation of the signal from a picture I’ll add). I was ...
31 views

### Relationship between different 2D FFT/Fourier domain window sizes?

hope everyone is enjoying their holidays. I'm a PhD researcher and I have an idea to filter an image using FFTs but I would like to try capture information at different scales using multiple window ...
49 views

### Is Hann-windowing applicable when calculating a DTFT?

I have read that people often use a zero-padded DFT with Hann-windowing to get the amplitude+phase information at one frequency (where the Hann window is used to reduce the effect of a small/finite ...
681 views

### What is the energy`correction or amplitude correction for a Tukey window?

From this page: https://community.sw.siemens.com/s/article/window-correction-factors there is a list of correction factors for popular windows. Is there a correction factor for Tukey window, depending ...
161 views

### How does applying a unity-gain Hann window to White Noise change its power?

What works: I generate real-valued white gaussian noise with standard deviation $\sigma$ I calculate the FFT of this noise. The Abs of the FFT is a flat noisy trace over frequency, as expected for ...
300 views

### Window gain factor and amplitudes in FFT

I have some vibration data (acceleration) on which I need to perform an FFT, integrate it and again do an FFT. I read that for the nature of the data that I have, the input to the FFT must be first ...
227 views

### Applying Kaiser Window to sinc interpolation

I am trying to apply the kaiser window during sinc interpolation. The following is my sinc interpolation code: ...
1 vote
47 views

### Overlap correlation indices in Harris 1978

In the heavily cited paper by Harris 1978, there is a section on "Overlap Correlation" where he's using a "fractional overlap r" in his equation. Here is a screen shot from the ...
90 views

### Window Choice of FFT

I am working with data from a TeraFlash THz Spectrometer from Toptica, which gives me the pulse in the time domain and the spectrum in the frequency domain I have been experimenting with the FFT to ...
628 views

### Number of periods of signal required when doing an FFT

I'm using numpy.fft in python to compute Fast Fourier Transforms. In particular, I'm using rfft as I have a real signal and don'...
333 views

### How to generate a raised-cosine window with a specific roll-off factor in Matlab?

I have recently started working on signal processing. For a small project, I have to shape cosine signals using a raised-cosine window with certain roll-off factors in Matlab. To give you an example, ...
155 views

### Impact of STFT window function and FFT length on computation time

I have been doing a study which part of it includes a comparison of computation time vs window type and length (among some other things in the computation time, however I speak in terms of relative ...
121 views

### Sampling, filters, windowing, FFT. From theory to help on this coding list

My plan is to analyse the spectrum of samples from a microphone. I wonder how correct this suggestion is. The below description may then fail on several points. I am in need of somebody with a red ...
463 views

### Applying a window to a signal

How can I Gaussian or Bartlett window to a signal? On the other hand, is it a good way of smoothing signals? If not what are the differences between smoothing and windowing?
437 views

### FFT with High Time and Frequency Resolution

Can anyone describe in a bit more detail or provide references to the techniques for simultaneous enhancements to time and frequency resolution described in a high level in HEAD acoustics ...
367 views

### Low-pass vs. windowing function in front of FFT

I am sampling sound at 48 kHz because that's what the DAC for the headset needs. I take every 6th of these. So I have 8 kHz and process 1024 at a time. My goal is to analyse the spectrum in the final ...
253 views

### Complex Windows

Typically windows are symmetrical and real. Are there any applications where complex windows have been used (other than applying the same real window to the real and imaginary components of a complex ...
76 views

### Understanding spectral leakage in a pink noise dominated signal

I've been reading about power spectral density estimation based on the DFT, about spectral leakage, windowing functions and the Welch method. I've recorded a signal that's supposed to be pretty much ...
492 views

### normalize STFT output by magnitude

I am using torch.stft() to generate spectrograms for neural networks and come across the below code. ...
298 views

### Optimize window length (STFT) via gradient descent (in neural networks)

The authors from this paper optimized a Gaussian window size via gradient descent (the σ parameter of the bell curve) together with the other parameters of neural networks. I don't use Gaussian window ...
1 vote
249 views

### Artifacts on frequency spectrum

I made a spectograpm in C that takes in a wav file (44.1kHz), converts it to 8bit pcm(can't go higher because of memory constraints) and does 1024 sample FFT on a number of bins, using Welch method. I ...
1k views

### Proof that the rectangular window has the best resolution

The resolution of a window is typically defined by the width of its spectral mainlobe (3dB-width or null-to-null width). It is often stated that the rectangular window has the best resolution among ...
186 views

### lopsided Hanning Window function

I am processing sensor signals and have been looking at using window functions to smooth out the signal before I conduct a fft on it. A normal symmetrical hanning function seems to disorientate the ...
95 views

### Graph Plot On Time Shift of Cosine Signal Hanning Function

I am plotting time shift of the Hanning function. I find few plot result that I am not able to understand. Therefore I would like to ask my question here. The given Hanning function is:  x(t)={\tt ...
80 views

### Under which conditions will windowing with a rectangular window intime always lead oscillations in the spectrum?

I'm going through some conceptual questions about windowing signals. I came across the following: Assume a sinusoidal signal - under which conditions will windowing with a rectangular window ...
1 vote
308 views

### Direct calculation of the fft of a rectangular window

For a rectangular window defined as, the frequency spectrum equation and magnitude (or pseudo-magnitude) plot are, However, when I apply Scilab's fft() function or the definition of DFT definition ...
191 views

### Window with optimal sidelobes for a given ENBW / frequency-resolution

Is there a family of windows which is "optimal" in terms of energy above/below a boundary, but with controllable ENBW/bandwidth? By optimal, I mean maximising energy concentration inside ...
1 vote
668 views

### sensor data windowing and normalization

I am getting up to speed with working with sensor accelerometer data. I am looking to conduct a FFT on this signal. I found that the signal being non periodic is causing issues so I have tried to look ...
1 vote
255 views

### Plot of the Fourier transform of the Sine Window

In Wikipedia, a Fourier transform of the Sine Window \begin{align} w[n] = \sin \left(\frac{\pi n}{N} \right), \ 0\leq n \leq N \end{align} is plotted like below. However, I am not sure how to obtain ...
1 vote
1k views

### Do we guess the cut off frequency when passband edge frequency and stop band edge frequency are given? FIR Filter design-LOW PASS FILTER

Say passband edge frequency=0.25 $\pi$ Stopband edge frequency=0.35 $\pi$ What is the cut off frequency? Do we average these 2 frequencies and write the answer or what is the procedure to find cut off ...