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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ENBW for non-white noise condition
The usual defininition of equivalent noise bandwidth (ENBW) seems to include a white-noise condition. However, say I know the noise spectra of my signal is distributed differently, say pink noise. ...
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IFFT of signum in Fourier domain
The continuous Fourier transform of the signum function ($\text{sgn}(x)$) is $\frac{1}{i\pi \xi}$. If I simulate this function in MATLAB and perform an IFFT (a discrete, time limited Fourier transform)...
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Reason behind Window function in STFT
Ive been digging the area of stft analysis of discreet time audio signals.
One thing I still can't understand is this - it is common to use window function such as hann, hamminh etc. When doing stft, ...
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Prove that the Fourier coefficients of the Dolph-Chebyshev window are positive
Suppose parameter $x_0 >1$, integer $M \geq 1$. Let $T_n(x)$ denote Chebyshev polynomial of the first kind, with recursive relation: $T_0(x)=1, T_1(x)=x, T_{n+1}(x) = 2xT_n(x)-T_{n-1}(x)$. The ...
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When to use symmetric vs asymmetric (periodic) window functions?
Libraries like scipy typically offer constructing window functions in a symmetric or asymmetric flavor. I'm aware of the rule of thumb:
Use symmetric for filter analysis.
Use asymmetric for spectral ...
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What is the "general effect" when a signal's frequency component falls onto the boundary of two neighboring DFT bins?
Imagine I have a perfect 1 Hz continuous signal that I sample at 100ms intervals for one second (this gives me 10 samples in total) If I perform a DFT on this and only look at the positive frequencies,...
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Designing a flat-phase DFT / DTFT window
Problem
I have a sampled time domain record of a signal with unknown, but constant frequency and amplitude, superimposed on a roughly white-noise background in the relevant frequency range.
I now want ...
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High Precision Measurement of Both Magnitude and Phase of Intermodulation Products
I need to measure (with high accuracy) magnitude and phase of some intermodulation products generated by a non-linear analogue device (black-box).
The input signal consists of two tones at very close ...
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Showing analytically that sampling exactly 1 period of a sinusoid yields a spectrum with no lobes in the DFT
The DTFT of a discrete sinusoid $f[k] = \sin(\omega_0 k)$ is
$$F(\Omega)=i\pi(\delta[\Omega-\omega_0] + \delta[\Omega+\omega_0]), \: \: \: \Omega \in [-\pi, \pi)$$
The DTFT of a rect function $w[k] = ...
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Comparing the Order of STFT and Windowing in Audio Data Preprocessing for Machine Learning: Which Approach is Better?
I am designing a machine learning preprocessing pipeline for a time-series dataset and came across this paper. In the paper, the authors first apply the Short-Time Fourier Transform (STFT) to the ...
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Why is Hann windowing identical to convolution with [-1/4, 1/2, -1/4] in the spectral domain?
I'm trying to understand why multiplying by a Hann window in the time domain corresponds to convolving with the kernel [-1/4, 1/2, 1/4]. I've put together the following chain of reasoning, but I have ...
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Hamming Window FPGA Implementation
Like to implement it in FPGA should i just store the Hamming Window coefficients in ROM (so in memory),
And since my input data(that i will feed into hamming window) are sequential ,I will just ...
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What does resolution mean in the context of Gabor limit or in context of windowing?
I am trying to understand why there is a tradeoff between sidelobes and main lobe width. This answer explains really well but I don't understand what resolution in time domain means.
From my ...
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Sliding window with fading tail
I am new to signal processing. So far, I know how to analyze time series of a signal using a sliding window and I have used that approach before while analyzing a signal in frequency domain to improve ...
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Artifacts introduced by Fourier Transform
I am new to signal processing. My background is Petroleum engineering, however I am concerned with analyzing acoustic data for some applications. I am using Fourier transform to transform signal from ...
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Which FFT Window to use for data gathering of complete mastered songs - for AI
I have a novel technology that I developed, which I plan on incorporating AI beginning with simply recording a basic machine learning strategy of Input - Output for eventual training.
In this case ...
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How does MATLAB's edgetaper function work?
MATLAB has a function edgetaper that does something I haven't seen before:
J = edgetaper(I,PSF) blurs the edges of the input ...
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Differences in PSD for windowed vs non-windowed spectra
For a non-windowed spectrum, this article gives this equation for the power spectrum $$\text{PS}(k)=\frac{1}{N^2}|X(k)|^2$$ and this for the power spectrum density $$\text{PSD}(k)=\frac{N}{f_s}\text{...
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Why doesnt DFT Padding cause sinc like features
I'm new to the land of DSP so any incorrect terms please let me know.
It seems padding the time domain signal can make the magnitude spectrum look 'nicer', the fact it doesn't gain any more useful ...
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How to find frequency , location and phase of two sinusoid signal buried in noise?
There is a data set which has two different sinusoids buried in noise. Data record has following properties:
A data records with a total data length of 2048 points.
The sampling frequency is 100 Hz.
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Looking for an online course
I work for a company with expertise in electromagnetics physics, specifically dealing with time domain-based simulation software. We routinely need to transform our results into frequency domain, ...
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Calculating stopband cut-off frequency and stopband attenuation for FIR lowpass window filter
I am aiming to create a digital windowing FIR filter on MATLAB and have been given specs such as a:
sampling frequency of 360Hz
maximum filter order of 5
cut-off frequency of 98Hz/ 1.710rad/sample (...
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Filter coefficients hamming window for low-complexity Welch PSD computation
I am trying to implement the proposed method from this paper 1, to eventually have a more efficient PSD computation for feature extraction on a microcontroller.
The method is suitable since I am using ...
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Speech Endpoints Detection using Explicit approach
The "Fundamentals of Speech Recognition" text by Rabiner, mentions three approaches for Speech (Endpoints) detection - Explicit, Implicit, and Hybrid approaches. I am studying the block ...
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Why is there a tradeoff between simplicity of a window function and its ability to be adjustable and controllable?
While studying and applying different window functions in a project I am working on, I found that known windows (here is an example paper which cataloged numerous windows) suffer from 2 kinds of trade-...
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Window function with no sidelobes
I found the Hann–Poisson window on Wikipedia. It has no sidelobe for $\alpha \ge 2$.
I am interested to know more examples of such window function with no sidelobes and what they are useful for.
I ...
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What are the *undesirable* effects of windowing in Fourier space?
My goal is to split a periodic signal into two (or more) signals. The first signal would contain the low-frequency information, and the later signals, the higher-frequency information. These signals ...
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Taylor Window Algorithm
I am trying to find out the algorithm for taylor window function but i have looked everywhere and i dont see any proper algorithm.
I read it is similar to Kaiser Window but thats all I know.
Can ...
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Why window functions can't have both narrow main lobe and low-level side lobes?
Why window functions can't have both narrow main lobe and low-level side lobes?
i got a hint from my mentor that it's quite often expained in books about wavelets...
I thought it could be associated ...
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What can be done, on top of windowing, that can reduce spectral leakage?
I am relatively new to DSP, and I am trying to create a spectral suite plugin using the IPlug2 library for creating vst plugins, and an FFT library I found on GitHub.
So far, I can perform an FFT on a ...
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Welch method implementation not smooth
I have been trying to recreate the welch method implemented in scipy.signal by hand but my results don't look close enough in my opinion. How come the scipy.signal.welch method is displaying much ...
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Calculating the main lobe width of Dirichlet kernel
The Dirichlet kernel of order $N$ is defined as:
$$
D(\theta,N)=\frac{\sin(N\theta /2)}{\sin(\theta /2)}
$$
We know that the main lobe widths between zero crossings is: $4\pi/N$
I was wondering if ...
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FFT Window question - high resolution windows
So I am pretty familiar with FFTs and FFT windows. I know that in general there is a tradeoff between mainlobe width and sidelobe levels.
However, I recently stumbled across this discussion, where ...
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What window functions allow for controlling the location of nulls?
Window functions are commonly used to control spectral sidelobes. Typically there is a trade between supressing sidelobes, and maintaining the resolution of the mainlobe. A window with lower sidelobes ...
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Decreasing gibbs phenomenon with window functions multiplied in time domain
I know about using fitering(e.g. window filters that used in frequency domain), wavelets for decreasing or even full eliminating gibbs effect but don't really understand how we can use window ...
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How to adjust the length of the window of the Fourier transform with respect to the length of the signal in Python
I ran the following code in Python, setting the window length to 5s, but he reports an error as the window length does not match the signal length. How should I adjust it please?
code:
...
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Noise spectral density and windowing
I am wondering about the definition of Power Spectral Density, in the context of measuring noise, i.e., Johnson-Nyquist (thermal) noise.
Usually a windowing method, like Welch's method, is used to ...
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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....
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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