# 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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### FFT/PSD/IFFT analysis on single axis piezoelectric accelerometer signals for curb impacts

I'm trying to denoise the signal by performing PSD analysis and followed by IFFT. Ultimately, I want to generate Force and Displacement plots from the denoised acceleration signal. Noisy Acceleration ...
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### 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 ...
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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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### How to determine number of filters in filter bank based on spectrogram of audio signal?

I want to do an analysis and than synthesis of audio signal, which is audio of vowel 'a', using Matlab. For this I need to use filter bank(array of band-pass filters). I have drawn four different ...
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### Smooth signal with Hanning

I have an acceleration record and i want to smooth it's spectrum by using a hanning window with Bandwidth=0.5 Hz. How could i do that? Example in python/matlab will be appreciated!
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### 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 ...
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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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### Increasing the number of points in the frequency spectrum

I have an image with few pixels in length and height. For this image I calculated the two dimensional Fourier transformation. What I got for the frequency spectrum in one direction was a very ...
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### 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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### 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 $N+L-1$ ...
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### FIR filter design using Kaiser window - passband ripple and stopband attenuation

I have been given the following parameters : lower cutoff frequency = $\pi/3$ lower cutoff freq = $2\pi/3$ beta = 5.6533 M = 51 Now I have to get magnitude and phase response of the filter using ...
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### What's the ideal FFT window for measuring a group of signals of differing amplitudes but close in frequency?

In my system, I need to measure the amplitudes and phases of four lasers, each of a different, known wavelength, chopped at a 50% duty cycle via TTL at frequencies spaced evenly (or not) around some ...
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### Find Magnitude of a DFT signal using a Blackman window

Hi I've been given a signal made of a series of cosines. I have taken the DFT of the signal using a rectangular window (blue), hamming window (red) and a Blackman window (black). I have identified two ...
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### What is appropriate windowing technique for sine burst excitation?

I had to give sine burst to get good SNR. In above Blue color -> Actuation signal or input. Orange -> Response or output. I did use hanning window for both. The frf real & imaginary plot ...
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### Computing main lobe width of Hamming window in Matlab by plotting

I wanted to verify the fact that main lobe width of a Hann/Hamming window is twice that of a rectangular window, using Matlab. I computed the analytical expressions for the respective frequency ...
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### MATLAB Hamming window

I have been trying to achieve a Hamming window length of 23 using the equation. I tried several coding, one of the is the one below: ...
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### Coherent Sampling vs Windowing for 50/60 applications

Let's say I need to sample 50/60 Hz signals to find RMS. I can use for example 1kHz sampling frequency. That means 100ms sampling is 5 cycles of 50Hz and 6 cycles for 60 Hz. That's coherent sampling. ...
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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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### What is the spectrum of generalised periodic signals assuming mainlobe covers the first two harmonics?

I found this statement in the paper here which I have difficulty seeing why is it true. Let $H(\omega)$ represent the Fourier transform of a time-windowing function. Assume the width of the mainlobe ...
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### spectral leakage for integral number of periods

I'm attempting to understand spectral leakage and read the following quote on wikipedia: Windowing a sinusoid causes spectral leakage, even if the sinusoid has an integer number of cycles within a ...
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### Is the DCT prone to spectral leakage like the DFT?

My understanding is that the DCT assumes the input to be an even periodic signal. This avoids the discontinuity that can occur in the periodic extension assumed by the DFT (see image). Does this lack ...
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### Windowed N-point FFT

In the previous question, Smoothing in frequency domain and impulse reponse of the filter in time-domain I guess I have made a mistake in-terms for applying windowing to FFT. After reading "...
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### Is the discrete Gaussian kernel an eigenfunction of the DFT?

So the Gaussian function is an eigenfunction of the Fourier transform because it transforms into itself, right? But this isn't true for the sampled Gaussian in the DFT because the tails of the ...
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### Variable Window Size of Blackman FIR filter

I am trying to implement an FIR filter with a Blackman window function. The solution I got for my signal filtering problem is to have different window sizes for certain characteristics of the input ...
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### 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?
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### Zero Meaning a Hamming Window in Matlab

I am still relatively new to signal processing and MATLAB and am working on a short-time fourier transform of some data using a prexisting code. Within the code a Hamming window is produced and ...
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### FFT result of windowed cosine function

The frequency spectrum of cosine function is as below. While adopting a square window function to the cosine function, it is same as implementing convolution of their frequency spectrum as below. The ...
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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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### Reconstructing a signal from multiple filtered copies using overlapping tapered windows

I have an audio signal that I need to process and analyse in blocks. I've now decided to process it using overlapping non-symetric Hanning windows of length M = 9600 and a hopsize of R= M/2. I zero ...
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### Why could window function help to get more accurate specific frequency amplitude?

In order to calculate amplitude of sinusoidal signal at a frequency around 60 Hz (but may be not 60 Hz), window function is adopted while using DFT. hk is the coefficient of window function and Kdc ...
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### How to removed ripples cause by zero-padding in fft?

Desired outcome: Interpolation in frequency domain Attempts: Zero padding when doing fft Problem: Ripples in frequency domain appeared after fft with zero padding Code to reproduce the problem: ...
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### Gibbs phenomenon, which window to use?

"Rectangular window" and "Triangular window" have gibbs phenomenon So which window should be used in fir filter design to have minimum or zero gibbs phenomenon
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### Confusion calculating length of Kaiser window

I am reading Digital Signal Processing Using Matlab by Ingle and Proakis (3rd ed.) In Chapter 7, Section 7.3, I am confused why he is adding 1 to main lobe width for calculating length of window. I ...
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### Advantage of applying a Window Function in Analysis and Synthesis of STFT?

I'm studying Short-time Fourier Transform and I learned that if you apply a windowing other than rectangular, you need to overlap the frames---for example, 50% overlap for Hamming family---to ...
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### Compute Hann window without cos function

In an environment with limited memory and computing power it is interesting to be able to generate a Hann window without using a cache or repetitive calling of expensive functions such as sine and ...
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### 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 ...