# Questions tagged [sampling]

In signal processing, sampling is the reduction of a continuous-domain signal to a discrete-domain signal.

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### Alignment of 2 Set of Samples from Different Sensors

If we measure the heart rate of a subject with two different devices, which have big different sampling rates then how we can compare their outcomes. For instance, one of the devices has the sampling ...
248 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 ...
3k views

### Is sampling at double the desired reproduction frequency accurate?

This is probably a general principles question, though I'm thinking specifically in relation to sound, which is commonly sampled at a rate of 44.1 kHz in part because the maximum frequency the average ...
1k views

### How does the number of frequency-domain sampling points influence the outcome of an inverse FFT?

Given some frequency-domain representation of an impulse response. How does the number of frequency-domain sampling points influence the outcome of an inverse FFT, if I keep the sampling frequency ...
640 views

### What is the most computationally efficient way to generate 100 sine waves layered on top of each other?

Right now I simply do this (pseudocode) for freq in freqs: for i in len(samples): samples[i] += sin(...) Is there a better way? This is for ...
321 views

### If sampling rate is high does that increase the error or decrease the error?

Suppose we are tracking a computer mouse on the screen, if we increase the frequency of the sampling rate(to very high values) then would that increase the error in getting the exact position of the ...
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### Envelop detection with low sample rate?

I have a signal up to $3\textrm{ MHz}$. The ADC that sample it has a rate of $1.5\mu s$. So a full $T$ of the signal is $0.3\mu s$, and I can only sample each $1.5\mu s$. It sounds not enough, but I ...
274 views

### What is the frequency of $\cos x -\sqrt 2\cos\sqrt 2 x$?

Question Considering that $1\over{2\pi}$ is the frequency of $\cos x$ and also of $\cos x - 2\cos 2x$, what is the frequency of $\cos x - \sqrt 2\cos\sqrt 2 x$? Thoughts Perhaps "frequency" isn't ...
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### pitch vs playback rate

Let's say I have an audio sample, whose pitch is known to be C4 (don't wanna go in detail here, let's say I just sampled a tuned piano playing the C4 key). The rules of the game are: I can only ...
75 views

### Nyquist Rate (Sampling Frequency) for ${f}^{2} \left( x, y \right)$

We are given that $f(x,y)$ is highest frequency is $\omega$ what will be the frequency sample rate if we want to restore the function of the form $g(x,y)=f^2(x,y)$ Would it be correct to say that ...
373 views

### Noise PSD and sampling rate relation

Let's consider generating samples of a random process like white Gaussian noise (AWGN). Let's assume I am generating $N$ samples of AWGN with variance $\sigma ^2$ in MATLAB by using randn() funtion i....
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### Sampling and Reconstructing Digital Signal

Say that I have a digital signal (a bitstream actually) whose output changes every 100 mS. I don't know exactly when it changes relative to my sampling, only that that the next bit to capture appears ...
2k views

### Fusing or combining signals from multiple sensors

I've become very interested in the problem of fusing multiple low-cost sensors' outputs and trying to combine these outputs in such a way as to rival or exceed the output of a single high-quality / ...
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### What are some deep results in sampling theory?

I have taken a basic course or two in signal processing and I've seen the Nyquist sampling theorem - an interesting and surprising result giving sufficient conditions for reconstruction of a ...
167 views

### Codec Output has “Wavy” Amplitude on Chirp Input

I am sending a chirp that sweeps form 20Hz to 500Hz to an audio codec, CS42L52, connected to an MCU, STM32F405, and I am receiving a "wavy" amplitude output. There is no processing on the MCU, I pass ...
146 views

### About sampling and wireless networks

Wireless networks operate on a high frequency, say some several gigahertz. Are the signals really sampled at that high frequencies? If I got it correctly there's some modulating/demodulating in signal ...
184 views

### What is the optimal adaptive grid for calculating a DFT using a fixed number of sampling points?

I'm currently facing the following problem: I want to approximate the Fourier transform $F(\omega)$ of a (let's say, $L^2(\mathbb R)$) function $f(x)$ by calculating the discrete Fourier transform, ...
239 views

### Locking on to a square wave signal with minimum oversampling

I'm designing a device that will have an IR photodiode connected to a low power microcontroller's ADC pin. At times, another device will be transmitting a 48KHz square wave, and I'd like to be able to ...
86 views

### Multiplying signals in discrete-time vs continuous-time

Given two discrete-time signals $a[n]$, $b[n]$ and its product $c[n]=a[n] b[n]$. The ideally interpolated, continuous-time version of $c[n]$ is \begin{align} c_1(t)&=\sum_{n=-\infty}^{\infty} a[n] ...
117 views

### Understading sampling theorem and aliasing

A real-valued analog signal with a flat spectrum between f = 0 Hz, and fmax is sampled at a sampling frequency fs = 24 kHz. The sampled signal is then processed with an ideal lowpass filter with ...
90 views

### How to undo dynamic Doppler effect by software?

I have a signal affected by Doppler effect. In general, the Doppler effect changes the scale of the time and frequency domains. So, to undo this phenomenon, I am using a sampling rate converter. Two ...
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### Gaussian Pyramid - How is Subsampling Rate Related to Sigma?

I found a gaussian pyramid implementation in a MOPS paper (feature detection). They use sampling rate $s=2$ and $\sigma=1$ - i.e. to generate a new level of the pyramid, the current level is smoothed ...
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### Understanding “voltage” and “power” in SNR of a sampled signal

I'm facing a gap in my understanding of when a signal is a "voltage" signal and when it is a "power" signal that I've always managed to avoid resolving until now... First what I think I understand, ...
617 views

### Benefits of oversampling in a realtime noise-cancellation system

When sampling a signal, it is standard practice to use a sampling rate that is greater than two times the bandwidth of the signal in order to avoid aliasing. The result is then low-pass filtered (and ...
1k views

### Using Goertzel Algorithm in under-sampling

I plan to calculate a signal's phase using Goertzel Algorithm. I have 2 signals coming to microcontroller's ADC. Need to measure the phase difference between them. Signals are 15MHz sinusoids. Sample ...
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### Why do we read that Hilbert transform can be used for envelope detection?

We can often read that Hilbert transform is useful for envelope detection (e.g. Hilbert transform to compute signal envelope?) I have done some tests with various soundfiles, and ...
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### Representing a continuous LTI system as a discrete one

I am aware that there are different ways to represent a continuous time system in discrete domain (e.g. bilinear transform, impulse invariance transform). But my problem is as follows: Given an ...
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### Minimum time delay that can be estimated between two sensors

Consider a 1-dimensional toy problem. I have two sensors at different points along the $x$-axis. Somewhere away from the sensors, a disturbance is created which travels towards the sensors, first ...
944 views

### Sinc interpolation formula for signal reconstruction in frequency domain from bipolar samples

As per the title, I was wondering if there was a $\operatorname{sinc}$ based interoplation formula for reconstructing a signal in the frequency domain which has been sampled with respect the bipolar ...
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### Aquila DSP C++ Library - Wave file FFT analog frequency off by factor of 4?

I'm working with the Aquila C++ DSP library. I'm computing the FFT of a wave file (16 bit depth, single channel, 44100 sample rate). I am using a window size of 16384 to calculate the FFT spectrum. I'...
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### Interpolating on the borders of differently-resolved images

I'm creating a three-dimensional model of the earth based on SRTM height data. The data set is pretty huge, so only a small fraction of the data is available at any given time. The height data is ...
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### Mathematical model of equivalent-time sampling, the resulting unevenly spaced periodic signal, and its interpretation

I sample a continuous signal $s(T)$ over time. This leads to $s[t]$, which depends on several factors of which some are (pseudo-) periodic. I am interested in the effect of one such periodic factors ...
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### understanding discrete wavelets

I was reading section 4.3.3 from chapter 4 of "A Wavelet Tour of Signal Processing", "...Let $\bar{f}(t)$ be a continuous time signal defined over $[0,1]$. Let $f[n]$ be the discrete signal obtained ...
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### A question about sampling rate of cosine signal

Given $$c(t) = \cos(2\pi\cdot 30 \cdot t)$$ If we sample this signal at the Nyquist rate 60 Hz and at a higher rate of 80 Hz, we get the following: There is no aliasing as $f$ = 30 Hz is less than ...
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### What sample rate should I use on my ADC?

I have an ADC that will have a guitar track as an input. I want to find which notes are hitting via the frequency domain. Given that guitar frequency range is from 82Hz to 1046Hz which sample rate (...
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### Sampling: question regarding sampling period

what exactly happens when I increase the sampling period ? Providing some Matlab plots so that I can be more clear. Using the signal $x(t) = \sin(10\pi t)$ and periods $T_s=0.02 ,\; 0.05 ,\; 0.1$ ...
213 views

### What is the role of a LPF in oversampling?

Lets assume that a signal $x(n)$ is up-sampled by adding 1 zero between two adjacent samples to form a signal $y(n)$. How does a digital LPF give an oversampled version $z(n)$, with more data points? (...
Given a known signal $x \left( t \right)$ and its delayed version $y \left(t, \tau \right) = x \left( t - \tau \right)$. Both are sampled by Sampling Frequency ${F}_{s}$ to generate the signals $... 2answers 3k views ### Can the order of filtering and downsampling be exchanged? Say for example, I have a signal with maximum frequency at 600Hz, and I originally oversampled it at 2000Hz. Afterwards I was only interested in frequency less than 500Hz. I guess I could first filter ... 2answers 3k views ### Sampling a Unit step function I have following two related questions concerning unit step function. 1-I want to sample the following signal. What will be the sample value at t=0? The signal takes 0 time to change from 0 to 1. So ... 1answer 329 views ### Understanding the mathematical proof for the alias frequencies in a sampled sine wave I'm struggling to get my head round the mathematical proof for the alias frequencies in a sampled sine wave. I understand that sampling a sine wave of frequency$f_0$every$t_s$seconds gives you:$...
A signal $x=\sin(\pi t/4)$ sampled at every $t=1$ sec. so $T=1$ sec Sampled signal is then $x=\sin(\pi n/4)$, What is the sampling rate in this case?, And according to Nyquist sampling rate what ...