# Tagged Questions

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

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### 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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### 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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### Upsampling and windowing

Let's assume that $k$ represent a tone (i.e. frequency) index and $n$ represents time index. After upsampling the signal $V$ times,i.e., adding $V-1$ zeros between each two samples I get a following ...
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### 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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### 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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### Windowing the sequence to compute Correlation

I want to compute the Correlation Functions of the input and output time-domain sequence, ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### Applying window function to Gaussian Like distribution

I am trying to calculate the Modulation Transfer Function (MTF) for a CT scan. I get use the differential of multiple line profiles (as recommended by International Electro technical Commission (IEC))....
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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 ...
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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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### 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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### Windowing function squared?

Reading this paper about WSOLA (Verhelst, Roelands) 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 squared. ...
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### Running window maximum: Any cautions?

Are there any statistical concerns with using a running-window maximum to capture peak values? Background: We are measuring acceleration during random impacts on a structure. The impacts need ~500Hz ...
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### Minimizing sinc spectral lobes

for some reasons I'd like to minimize the secondary lobes of the FFT transform of a rectangular signal (shwon in the upper-left side of picture below) so I've used window function to do that (bottom-...
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### python scipy fft on numpy hanning window smears peaks

I have a signal that I have acquired from an experimental instrument, that I wish to examine in the frequency domain. I don't care about phase for this exercise, I only care about magnitude. I ...
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### Applying a window to input signal

I am sorry if I say any thing silly .Please forgive me.I want to apply a window to input signals.I have two signals each of which contains zeros (462 samples) and non zeros data (38 samples).I want my ...
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### Analysis with Window before FFT

I have two signals $x$ (see below) and $k$ (obtained by giving circular shift of 106.5849 in $x$). Before I take FFT of both ($x$ and $k$) I want to do window analysis on them. Kindly can some one ...
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### 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-...
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### 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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### Non-separable, higher-order generalized cosine windows in 2D for images

Higher-order generalized cosine windows define a useful parametric family of windows functions, embedding Hamming, Hann, Blackman, Nutall, etc.: w(n) = \sum_{k = 0}^{K} a_k\; \cos\left( \frac{2 \pi ...
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### How is the ends of a bandpass filtered signal reliable after applying the cosine taper?

A taper function decaying to zero at ends such as a cosine window is routinely applied to the signal before bandpass filtering to reduce end effects. Obviously the window alters the waveform. So, as ...
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### is any filter whose impulse response has a discontinuity in the first derivative fundamentally high-pass?

a triangular (bartlett) window has a kink (discontinuity in first derivative). thinking in the continuous (not discrete) case, my intuition is that the fourier transform of any window with a kink ...
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### hamming window for LPC

I am working on a library for generating LPC for speech synthesis. I am currently using a hamming window for the spectral analysis which goes in 200ms blocks over the signal, and does the a-to-k ...
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### 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 ...
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### Hamming window for filtering unwanted terms

I am trying to filter off two unwanted terms in this frequency spectrum (the spectrum on top). First, I used a convolution between a rectangular window to make the unwanted terms equal to zero. ...
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### Apply the Hamming window to a sinusoidal signal

I am a novice in signal processing. I am writing a code to apply the hamming window to a sinusoidal signal. So first I have digitized my sinusoidal signal by choosing a sampling rate more than twice ...
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### Formula to get the sui length of Blackman Harris Window

I was reading that I can to obtain the (N) length of Window function. if I have defined: ...
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### How to Combine FFT Overlap Results?

We currently have C/C++ FFT code with Hann Window function support. For a large data (over 10,000) we want to split this into 1024 samples with 50% overlap. For each 1024 sample, we window and fft. ...
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### what is the preffered data and FFT length for blackman harris window for improving Accuracy due to ENBW Consideration of window?

for Rectangular window if data length is 1K then FFT Length Should be 1K FFT only because ENBW of rectangualr window is 1.0 but for Minimum 4-Sanple BlackmannHarris window is 2.0. so for improving ...
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### MATLAB : How to filter a data signal

I have a data signal (column vector) with N values taken over at specific sample rate (dx) at a fixed frequency. After taking the Fourrier transform of this signal and representing it in the Fourier ...
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### Reconstruction of a windowed signal (specifically Hamming windowed)

Wondering about the resconstruction of the input signal when an overlapped windowing function has been applied. I'm specifically applying a Hamming window with 50% overlap and I wish to reconstruct ...
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### Sensitiviy and Resolution in Windowing Functions

When I read the article Windowing Functions, there are two terms that are does not understanding them well, sensitiviy and resolution. I looked for this two terms on the web, And I conclude that ...
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### Discontinuity at the edge of Chebychev window

I am using Chebychev window for its narrow main lobe. The problem of chebychev window is that it has discontinuities at the edge, and it seems that Taylor window solves this issue. More detail: http:...
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### What windowed Sinc might be closest to a Parksâ€“McClellan low-pass filter?

In another question on dsp.stackexchange, a statement was made that the output of MATLAB firpm() or firls() for an anti-alias low-pass filter was "close" to the coefficients of a windowed-Sinc low-...
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### 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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### What is the cause of slow roll off of windowed filters

Exactly why using the of windowing function, such as Hamming or Blackman, causes a slower transition to stop band? Everywhere it is mentioned just as an obvious fact that this happens but I haven't ...
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### Audio output distorted with any FFT Windowing other than rectangular

For an experiment i have a simple application that takes a quadrature signal from a radio and then does the following: Complex FFT -> Inverse FFT -> Cartesian to Polar -> audio out If I tune the radio ...
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### Subsampling data: terminology

I'm writing software and the data reporting frequency is slower than the acquisition cycle, so effectively sub-sampling is being done. Different data types require different methods of sub-sampling ...