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1500 questions
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What happens if we change the limits of integral in Fourier transform?

By definition of Fourier transform $$X(\omega)=\int_{-\infty}^\infty x(t) e^{-j\omega t} dt $$ Now what will happen to the answer of transform for example in case of $x(t)= \cos(\omega_0 t)$ if limit is $0$ to $A$ instead of $-\infty$ to $\infty$?…
heavenhitman
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Why Zero Padding in the Center of the DFT Interpolates / Upsamples the Signal (Sinc Interpolation / DFT Interpolation / Periodic Interpolation)

I'm experimenting with the Inverse Discrete Fourier Transform. Starting from the two-cycles continuous $x(t)$ signal below: I have the discrete signal $x(n) = \{ 1, 0, -1, 0, 1, 0, -1, 0 \}$ leading to the 8 points DFT $X_0(n) = \{ 0, 0, 4, 0, 0,…
Sylvain Leroux
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Do $|s(t)|$ and $|S(f)|$ uniquely determine $s(t)$?

Consider a signal $s(t)$. My question is if you know $|s(t)|$ and $|\mathcal{FT}[s(t)](f)| = |S(f)|$ or equivalently $|s(t)|^2$ and $|S(f)|^2$ is it possible to determine $s(t)$? That is, is $s(t)$ uniquely determined by $|s(t)|$ and $|S(f)|$? My…
Jagerber48
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7
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Downsample: resample vs antialias fitlering + decimation

I have a discrete signal sampled @Fs. I need to downsample it to Fs/k. Main reason is to reduce signal bandwidth and speed up computation : I'm only interested in a reduced bandwidth < Fs/2k. Some high frequency noise >> Fs/2k can exist :…
rem
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7
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Ultrasound pulses and reflection problems

I am building a whiteboard to track the position of its pen. I have n ultrasound receivers placed on the periphery of the whiteboard, and an ultrasound emitter in the pen. The pen emits pulses the receivers detect. A microprocessor gathers the…
Randomblue
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7
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4 answers

Are all LTI systems invertible? If not, what is a good counterexample?

I have been trying to figure this out for a while now. Everywhere I have looked I could easily find examples of invertible LTI systems, but I could not find any counterexamples. Can anybody shed some light on this for me?
Andrew
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Why the unilateral Laplace transform?

Why is the Laplace transform commonly taught as the unilateral Laplace transform? I mean, for the Fourier transform, we commonly have the bilateral transform... if the signal is 0 for $t<0$, then it turns into a unilateral Fourier transform. Why not…
Ameet Sharma
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7
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2 answers

Idea for Noise Level Estimation / Automatic Thresholding in the Presence of Peaks

I have the fft of some signal, and want a rough estimate of the noise level in order to choose an appropriate threshold for our peak detection algorithm. In general, the fft contains mostly noise with a handful of peaks (which are usually pretty…
Felix G
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7
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Losslessness of Laplacian Pyramid

I was just reading up on the Gaussian pyramid and the Laplacian pyramid, used in compression applications of image. The source is here - Carnegie Mellon 16-385 Computer Vision - Spring 2019, Lecture 3 - Image Pyramids and Frequency Domain. The slide…
Sridhar Thiagarajan
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7
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Compare image segmentation approaches

I've got a question related to a comparison of image segmentation algorithms. I'd like to compare two algorithm results to each other in step one. In another step I'd like to compare the two algorithms results against a few ground truth segmented…
mchlfchr
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7
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Why can adaptive IIR filters result in unstable solutions?

For adaptive filtering, both finite and infinite impulse response (FIR/IIR) filters can be utilized. As an advantage of FIR filters in this context, guaranteed stability is often mentioned, while IIR filters do not share this property (see this…
Jonas Schwarz
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7
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Daubechies Wavelet and Matlab

I want to use waverec to evaluate a linear combination of the scaled and shifted wavelet of the form $$ \sum_{i=1}^n\sum_{j=0}^{2^n-1}d_{nj} 2^{-n}\psi_{ij} (\frac{t-j}{2^n}) +c_{00}\phi(t) $$ at $t=k2^{-n} $ for $k=0\dots2^{n}-1$. I know how do…
warsaga
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7
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As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

There are several types of discrete nonlinear time-invariant systems with memory ("NTIM") which are considered "easy" to model and identify. Any such system can be represented using a Volterra series, but Volterra kernels become very difficult to…
Mike Battaglia
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Failed to implement Goertzel algorithm in Python

After some questioning on stackoverflow, I tried to implement a Goertzel algorithm in Python. But it doesn't work : https://gist.github.com/4128537 import math def goertzel(samples, sample_rate, f_start, f_end): """ Implementation of the…
sebpiq
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7
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4 answers

Is Fourier series a sampled version of Fourier transform?

I recently learned about dtft and how dft/dfs is the sampled version of dtft. I was wondering if Fourier series is also obtainable by sampling Fourier transform? I am a noob in the subject so sorry if this is stupid
Kartik Hegde
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