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Questions tagged [sampling]

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

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Nyquist frequency , sampling distance

I have few questions I tried to solve regarding nyquist theorem, and I would like to see your opinion if I'm doing it correctly?(one I know the answer second one not sure). 1.Let $f(x)$ and $g(x)$ be ...
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67 views

Nyquist sampling

I know that if $f_\mathrm{m}$ is the "Nyquist frequency" (max frequency) and $f_\mathrm{s}$ sampling rate then $f_\mathrm{s}>2f_\mathrm{m}$. Am I correct so far? I have a signal $x(t)$ with max ...
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26 views

What is wrong with my PSD computation?

I'm trying to calibrate the RX of my SDR Board to become a measuring receiver. I.e, by connecting it to a known source of power (in my case, a frequency generator), at a fixed frequency, I'm trying to ...
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10 views

TiVa C series123g [closed]

I had recently purchased the Tiva C series eval board for a project. Is there a way to implement a filter and an amplifier on the board itself and not with the help of hardware components?
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Definition of DSP Terms

can someone define/explain briefly (or with some detail-> up to you) the following terms: Block Processing? and what are the differences between it and Sample Processing? (removed) What is a 3D ...
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Sampling Frequency and Spectral Regrowth

Sampling a cosine wave of 10 Hz at Fs = 64 and number of samples Ns = 256 I setup my time vector for the cosine wave as n=(0:Ns-1)*(1/Fs) If I change the sampling frequency from 64 to 64.0005 I get ...
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20 views

Why is my resampled signal cutoff when resampling with a windowed FIR filter in MATLAB?

I have an exercise to write a function which upsamples or downsamples a signal by a factor of F (integer) using a FIR filter windowed with a Kaiser window function. Exercise I had last week included ...
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How to obtain the steady state response of the sampled periodic signal data?

Below the green plot Vin is 5Hz sine voltage signal from a function generator output sampled at 12kHz sampling rate: The blue plot Vout is the processed/filtered data by using the following code in ...
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Frequency Resolution Problem

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 ...
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1answer
40 views

Sample-rate, filtering, digital-filtering and aliasing

I am strugling with a question that I hope someone can help me with. I am recording single molecule events which I detect is picoampere square deflections. I wish to use as gentle low-pass bessel ...
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1answer
36 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 ...
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33 views

Calculate bandwidth of a signal for Nyquist–Shannon sampling theorem

I have to calculate the minimum sampling frequency for the Nyquist–Shannon sampling theorem which is Fc > 2*B, where B is the signal bandwidth. I have this signals: $\text{sinc}^5(t/2 - 4)$ and $\...
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18 views

What's wrong with this Whittaker-Shannon-Kotel’nikov interpolation implementation?

I tried to implement Whittaker-Shannon-Kotel’nikov interpolation formula but I get unexpected results: the reconstructed signal lags with respect to the original. I know that I can not expect a ...
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1answer
33 views

Sampling - Higher order harmonics

I have been studying about the sampling theorem and it seems that even though we sample at a frequency with the nyquist criterion, the harmonics (due to sampling process) remain within the nyquist ...
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95 views

What is the relationship between angular frequency and normalized angular frequency

This is a slide from my lecture notes: My professor used the following words " We denote digital frequencies with capital letters and analogue frequencies with lower case letters" The problem I have ...
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41 views

Proving Nyquist Sampling theorem for strictly bandlimited signals

I understand that the Nyquist sampling theorem dictates that the minimum sampling frequency, $f_s$, be s.t. $f_s > 2B$, where $ B $, is the bandwidth of the signal. I have read the explanation for ...
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Sampling and reconstruction of signal in Matlab

I'm trying to write a program in Matlab that samples (using Nyquist theorem) and recovers signal. I got stucked on recovery part...recovery signal doesn't match with the original one (see photo). And ...
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48 views

Fourier like spectral analysis with uneven intervals and redesigned DFT matrix

I intended to use a discrete Fourier transform (DFT) on a time series sampled at uneven intervals. What I did was to calculate a DFT matrix where the elements are the values at the uneven locations ...
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35 views

What does the frequency band mean when it comes to finding aliases?

The time signal which i'm trying to find the aliases for is: $$x:{\mathbb R}\rightarrow {\mathbb R}\\\ x(t)=\cos(50t) +2\cos(70t).$$ If the sample period is $T_s = \frac{\pi}{60}$ then according ...
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amplitude of upsampled and downsampled signal without filter

Given: $$ DTFT\{x[n]\}=X(\omega)= \begin{cases} 1 & |\omega| \leq 2/\pi \\ 0 & 2/ \pi < |\omega| < \pi \end{cases}\ \ \ \ \ (periodic\ 2\pi) $$ If I downsample $X(\omega)$ by M. I get: ...
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24 views

Frequency spectra of a sampled process

I have a process $X$ with frequency spectra I sample this process with sampling frequency $f_s = 2$. What will the frequency spectra $R_z(f)$ of the sampled process $Z$ look like? I realize that ...
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Isosurfaces from three dimensional column data: methods

I have just been asked the following question, and I somehow felt short of smart answers. You are given a series of $N$ triplets of values ($P_1$, $P_2$, $P_3$), pertaining to physical measurements. ...
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40 views

What is Finite Rate of Innovation Signal?

I have read about Finite Rate of Innovation signal by Martin Vetterli in here. But i do not understand several basic things The paper said that finite rate of innovation is the number of degree of ...
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29 views

How to simulate measured data with antialiasing filter

I wish to simulate measured data for developing signal processing methods. All properly measured data will have been through an antialiasing filter. How do I generate such simulated data? I have ...
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1answer
39 views

Choosing a Sampling Rate and a Cutoff frequency

I have an assignment: You wish to generate a pure 1000 Hz tone digitally using a computer. How would you choose a sample rate that assures that you could generate the tone and use the same sample ...
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1answer
31 views

upsampling for a signal

We have a signal $s(t)$. If we do an upsampling, does the signal duration increase? What is the point of upsampling if the signal time increases? Can we do an upsampling if we don't use a shaping ...
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58 views

Follow up question regarding: “Complex sampling can break Nyquist?”

I'm having some trouble understanding the sample rate limitations when considering a complex baseband signal. I understand (based on the linked SE questions below), the either (1) physically ...
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154 views

Passband vs Baseband Bandwidth

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. A key characteristic of bandwidth is that any band of a given width can carry the same ...
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1answer
56 views

Signals sampling

I have a simple question, but sadly I'm kind of "noob" in signals theory. A signal having 4 harmonics at the following frequencies: 1 kHz, 2 kHz, 3.5kHz and 4.2 kHz. (How can a signal have harmonics "...
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1answer
62 views

Are resolution increase and noise reduction from oversampling mutually exclusive?

Oversampling a signal means sampling it with a significantly higher sampling frequency than the Nyquist rate. As far as I know, there are three advantages: Easier design of anti alias filter Increase ...
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How to sample a transfer function (angular spectrum) in the frequency domain?

I am having this problem in Fourier optics, where I am using the Angular spectrum method (a lti filter) to calculate the electric field at the required plane given ...
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2answers
56 views

Nyquist Frequency Confusion

1- If I have a sine wave with period of $T$, I need to sample at least every $T/2$ to be able to reconstruct the sine wave. Let's look at this: This way I'd get a series of $0$s and all information ...
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Nyquist Theorem adding two same frequency near to Nyquist Frequency with phase shift

This is my first question on this platform. Sorry if I made mistakes. What happens if we add two or more same frequency signals near to Nyquist Frequency with phase shift and sample them? For ...
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54 views

Proving DSP Sampling Theorem [duplicate]

Schaum's Outline, Digital Signal Processing, Second edition, 2012, page 101: Prove that: $$X(e^{j\omega}) = \frac{1}{T_s}\sum_{k=-\infty}^{\infty}X(j\frac{\omega}{T_s}-j\frac{2\pi k}{T_s})$$
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Nyquist Theorem - Why unique frequencies upto Fs/2 and not Fs? f+Fs is start of Aliasing

If any frequency, f, displays an alias at f + Fs, This shows that unique frequencies have a range of Fs. Why does Nyquist theorem say that actually there is only half of this with unique frequencies ...
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1answer
18 views

Cancelling out known signal with sampling offset

I would like to cancel out a known audio signal at my receiver. Specifically at my transmitter I am playing a song, and at my receiver I am recording it. Both transmit and receive sampling rate is 44....
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Matching two signals with small time drift

I have two time-domain signals sampled at 100 Hz that were measured using two different oscillators and therefore have a time drift between them. I have two synchronization points, one at the start ...
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64 views

about sampling frequency

I am trying to make a DFT on a signal with frequency f=50 MHz main component plus some noise. As far as I know if I sample it at F=100MHz I should be able to get a proper plot of the DFT since F=2f ...
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1answer
42 views

What is normalized angular frequency? [duplicate]

I am new to DSP, and I am self-studying. I came upon this question, and I am stuck at it. Could someone please help me? Here is the question: In order to digitally create a sinusoid with frequency $...
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Definition of sampling using delta or indicator function?

I just came from a class where the professor showed a slide with the definition of sampling: But I do not understand how we can multiply a signal $x(t)$ with the delta function $\delta(t)$, as the $\...
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2answers
94 views

Plot the spectrum and n-point DFT

$x_a(t) = \cos(2\pi f_a t)$ was sampled with sampling period $T_s$. Plot the { spectrum | $N$-point DFT } of $x[n]$ ($f_a$, $T_s$ or $f_s$ given, $N$ given - whole number of periods or not). Anyone ...
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1answer
150 views

Why use a 1-bit ADC in a Sigma Delta Modulator?

When looking at the discrete model of a Sigma-Delta Modulator as shown below, we can see that the quantizer is modelled as a white-noise source $e[n]$. From this model, we can derive the noise shaping ...
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2answers
85 views

Sampling with an alternating impulse train

The have the following question: A signal $m(t)$ with bandwidth 500Hz is first multiplied by a signal $g(t)$ where $\displaystyle g(t)=\sum_{k=-\infty}^{\infty}(-1)^k \delta(t-0.5*10^{-4}k)$. The ...
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1answer
120 views

What is Faster Than Nyquist signaling?

Faster than Nyquist signaling is used to improve the spectral efficiency by reducing the time spacing (relaxing the orthogonality constraint) to pack more data in the same channel while tolerating a ...
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1answer
32 views

variance of the product of two samples with awgn

problem solved itself, sorry for your inconvenience. I'll try to post better questions next time.
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dsPIC33E ADC to FFT help

I am sampling an audio range signal with a bandwidth of 3100Hz and then applying a FFT using the DSP library example from Microchip to determine the most dominant frequency of the signal. On the last ...
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1answer
107 views

Applying Nyquist's sampling theorem to a real signal

I'm struggling to fully understand the Nyquist-Shannon sampling theorem. For some message input signal $m(t)$ that is infinite in time (i.e. is not identically $0$ for any interval $t_1<t<\...
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1answer
88 views

If my sampling rate is not high enough to capture all frequencies, can I accurately capture low frequencies?

Let us say that my sampling rate is 1000 Hz. This enables me to accurately capture every frequency in the 0-500 Hz range according to the Sampling Theorem using a DFT. However, there are higher ...
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2answers
66 views

Is it possible to discretely sample the function

I had a few questions on sampling(I'm quite new witht his), I tried to answer them, I think that I did the first one correct , but not sure about the 2 other: . given the next functions,Is it possible ...
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2answers
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How do MATLAB and/or Python treat $2^n$ samples rule in FFT

As far as I have read, an FFT requires that the number of original data points must be a power of 2. I'm wondering whether the tools like MATLAB or Python which have FFT functions take care of this ...