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3 votes
1 answer
172 views

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-...
0 votes
1 answer
506 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 ...
7 votes
1 answer
140 views

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 ...
0 votes
1 answer
243 views

properly windowing for better FFT signal

I have an analog signal as shown below. As you can see it has a DC component, a 1MHz component and some high order component. The period of the signal is 8.0199667µs. I want to see a good accurate ...
1 vote
0 answers
71 views

STFT normalization

In Scipy's implementation of STFT, an argument allows to scale the result as a spectrum or as a psd : ...
0 votes
0 answers
60 views

Power spectrum, Power spectrum density and windowing functions

At the moment I have some trouble understanding the different methods. I would like to calculate both the Power Spectrum and the Power Spectrum Density. As the name suggests I thought that $PSD = PS / ...
1 vote
1 answer
81 views

Can I apply an hilbert transform on a signal in subsegments [windowed hilbert transform?] [duplicate]

Consider I have a signal x which has N samples, N being a very large number. Could I create y, the analytical signal of x, by ...
1 vote
1 answer
79 views

Multiplying a finite signal with a unity window

I have a simple question to ask: Suppose $x[n]$ is finite and has a support for $|n|<L$ Let's denote its DTFT by $\operatorname{DTFT}\big\{x[n]\big\}(e^{j\omega})=X(\omega)$ Let's consider a unity ...
0 votes
0 answers
62 views

How best analyze a very short data record (~100 data points) windowing and padding data to perform CWT

I have short segments of a biological signal interpolated at 10 Hz (anywhre from about 8.5 sec to 10 sec length). I want to use a cwt to then convert this segment to frequency over the short time ...
2 votes
1 answer
188 views

upward shift in FFT windowed - attenuate fluctuation in FFT

I would like to limit the noise after the FFT. I have used this strategy: Divide the signal in segments using a Hann window Perform abs(FFT(segment)) Ensemble ...
0 votes
1 answer
36 views

Inverting the normalized Gaussian to get a kernel window radius

I am seeking to compute a kernel radius to use with my gaussian convolution filter, and inspired by https://stackoverflow.com/a/68050503/, I came up with: $$r=\sqrt{-2\sigma^2\ln\left( \epsilon\sigma\...
0 votes
2 answers
2k views

FFT of signal data with windowing, overlapping and averaging

This is my first ever question here so the help is really appreciated. I am performing FFT on a signal. I want to perform windowing, 50% overlapping and averaging to the signal. There is a function <...
2 votes
2 answers
225 views

What is the proper way to filter out unwanted noise from accelerometers?

I'm a beginner in signal processing and have a hard time to filter out environmental noise from the floor vibration data collected using accelerometers. I have tried using butterworth filter (IIR) ...
3 votes
2 answers
2k views

Hilbert transform with a sliding window

I have a input voltage signal which has disturbances present in it. I am actually discretizing the input signal into say $1300$ samples and taking Hilbert transform of the signal by taking $N$ samples ...
1 vote
1 answer
159 views

minimal signal window size (length)

In order to detect a frequency component of 1 Hz with a DFT - do I need a signal window (signal in time domain) of at least 1 second length (in order to have at least 1 cycle of the desired minimal ...
0 votes
3 answers
345 views

Multiple different length Windows for high resolution realtime FFT

I am looking at trying to achieve a 'realtime' (as quick as possible to acquire, process and present data) FFT application to analyse audio. I have setup my app to acquire a set of samples, apply a ...
1 vote
2 answers
2k views

How to design a lowpass filter using Hamming window and sinc function

I have these three equations and have a noisy voice signal. I have to design a low pass filter of length N=1000 using hamming window technique. I have selected its cutoff frequecny 0.25 (normalized). \...
-1 votes
1 answer
165 views

DTFT of window function applied to input signal

$$x[n] = \cos(\omega_1n) + \cos(\omega_2n)$$ $w[n] = 1/N$ for $0 \leq n < N, 0$ for everything else Find the DTFT of $y[n]=x[n]w[n]$ expressed by the DTFT of $w[n]$, $W(\omega)$ I was thinking ...
0 votes
1 answer
149 views

Yet another fft question - a vocoder

Lets assume a pipeline X: ...
10 votes
4 answers
11k views

What is Frequency Resolution?

Im trying to tackle the following problem while still not having a firm idea on what "frequency resolution" means : Suppose we sample a continuous time signal with sampling period Ts = 1/2000, and ...
2 votes
1 answer
294 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 ...
8 votes
2 answers
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 ...
1 vote
2 answers
4k views

Find the Equivalent Noise Bandwidth

I have already asked (in another thread) how to quantify (specify) the window function I have created. One figure I need it seems is the Equivalent Noise Bandwidth (ENBW) Or Noise Equivalent Bandwidth....
1 vote
1 answer
2k 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 ...
3 votes
1 answer
2k views

Use of Tukey window and its effect on a graph

I am trying to minimize the noise in a spectrum of a variable. I am trying to to divide the time history in equal parts, to do the FFT of this time history parts and to do an average between these FFT....
2 votes
1 answer
153 views

Biorthogonal Windows

I am starting to study about the concept of biorthogonal windows and the relation to (Discrete) Fourier transform and short-time Fourier transform (STFT). I have not found an introductionary review of ...
0 votes
1 answer
189 views

Confusion understanding phase shift/delay?

I am reading proakis, as shown highlighted in attached snap shot,there is '-'sign along with j,but still it is written (underlined red) implies shift in positive n direction,why and how positive?when ...
0 votes
2 answers
429 views

Windowing of signal before FFT

I am facing an interesting problem: I have a signal in the time domain. In order to avoid discontinuities at the edges of the signal --- which would lead to artifacts when calculating the FFT --- I ...
1 vote
0 answers
19 views

Apply window taper for selected window or to full data block in algebraic problem with known frequencies?

First, I'd like to introduce a problem. I try to solve a set of linear equations in LS (Least Squares) sense, i.e. Ax=y (LS) => A^TA x = A^T y. x is a vector I'm looking for, but y is a measured ...
5 votes
3 answers
550 views

Can I use more than one Window on an FFT?

I was wondering if it is possible to take a signal and run it through an FFT multiple times with a range of different windows, and then combine/average the results to get a more accurate Signal ...
0 votes
0 answers
86 views

Blackman window magnitude attenuation

I am trying to compute the fundamental phasor using sliding window DFT. I have employed a Blackman window in conjunction i.e $$ \sum_{k=0}^{L_{DFT}-1}x(k) w(k) e^{-j2\pi k/N} $$ where $x(k)$ is the ...
1 vote
2 answers
234 views

Windowing 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 $N+L-1$ ...
0 votes
2 answers
173 views

why is the signal divided into epochs in EEG classification?

I'm new in EEG signal classification. Studying the literature on this topic, I wonder why the EEG signals are divided in epochs, so, instead of classifying the whole signal all at once, we usually ...
0 votes
1 answer
132 views

Peak to Average Power Ratio of an exponentially increasing signal

I am having an exponentially increasing sinusoidal signal. After sampling, I am dividing the signal into frames of length 128 and doing windowing operation with a hanning window of length 128. Then ...
0 votes
1 answer
115 views

Discrete Signal Windowing

How do we apply windowing of 50% (4 samples) to a discrete signal with the odd number of values as 1234567? Is it done as: ...
0 votes
0 answers
38 views

How to specify a window?

I have developed my own window function for pre-processing signals prior to a DFT (FFT). How do I measure the performance of the window so that I can specify how good (or bad) it is? Maybe other ...
0 votes
1 answer
39 views

identify equilibrium region after large transient

I am looking at data from a mechanical system under an unsteady load. I'm trying to find the simplest way to identify the portion of the signal once the system reaches its new equilibrium. Here's a ...
1 vote
2 answers
99 views

Frequency Support of Window Functions

All window functions, which go from zero amplitude, up, then back to zero amplitude, are all base-band signals. Why is this? Are all functions that have this behavior always band-band aka low-pass?
1 vote
1 answer
132 views

Is it okay to interpolate between overlapping areas obtained using a sliding window?

I am using a 50x50 pixel sliding window which moves left to right every pixel so that it covers a whole binary image which is about 2000x2000 pixels. In the window, the ratio value of black to white ...
2 votes
1 answer
476 views

Why coherence function calculation needs averaging of different segments of the signal?

I am trying to understand coherence function calculation. I am working with a non-linear system without any noise. Coherence function is defined as: I understand that coherence is 1 for N=1, but I ...
1 vote
3 answers
2k views

Rectangular vs Hann windowing

I'm trying to create a basic digital signal processing pipeline, to manipulate a WAV file. Nothing fancy, I'm just looking to apply some filtering. My first attempt was to divide the input signal to ...
1 vote
2 answers
808 views

Multi Resolution STFT for audio

I am looking at trying to achieve a multi resolution STFT analysis on a log sine sweep audio measurement. I have an impulse, and I would like to perform two different windowed length FFTs on the ...
0 votes
1 answer
1k views

RMS from calculation from PSD using Welch's method [duplicate]

I've used Welche's method on a vibration signal to get the averaged FFT which I want to used to calculate the PSD from which I can calculate the RMS. Within the Welche method i've use Hann window ...
4 votes
3 answers
11k views

Understanding overlapping in STFT

I understand the concept of the STFT. In order to avoid spectral leakage, you use a Hann window that overlaps by 50%. However, the problem that I have, is that the example code online does not account ...
0 votes
1 answer
578 views

Energy using Hanning window

I am a newbie in signal processing. I am testing the Hanning window on a signal. Obviously doing this window also means cut some energy of the signal, and when I do the DFT, the 0 frequency is not ...
0 votes
1 answer
316 views

When can a windowed cosine be considered band-limited signal?

I have an exam in the following days and i have no clue of what is the response to this question in the exam: given this signal: $$g(t) = H\left(t+\frac{T}{3}\right) f(t) - H\left(t-\frac{2T}{...
1 vote
2 answers
699 views

Interpolated FIR filter group delay

I'm trying to design a digital low pass filter with a narrow transition band. My sampling rate is 25 kHz, the cut off frequency is 60 Hz & the transition band width is 4 Hz. I'm looking for about ...
1 vote
1 answer
181 views

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 ...
1 vote
2 answers
834 views

Half Window Functions and Formulas

I am looking at implementing different window functions in an application I am making. I have found the formulas for all major symmetrical windows, however I would like to implement half windows. ...
0 votes
2 answers
196 views

Bandpass Filter Order vs Sample Numbers of Noisy Signal

I'm working on signal filtering in MATLAB. i wrote sample code that generate 50 Hz signal with some noisy frequency and use Kaiser bandpass filter to get only 50Hz frequency. this code work great! but ...