Questions tagged [sampling]

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

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143 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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544 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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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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2k views

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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2answers
100 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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70 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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94 views

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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31 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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187 views

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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1answer
362 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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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
223 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
71 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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1answer
143 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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3k 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
93 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
393 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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139 views

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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3answers
582 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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1answer
73 views

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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104 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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356 views

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
56 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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129 views

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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1answer
150 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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226 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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3answers
169 views

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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253 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
406 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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1k 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
826 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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33 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
522 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
268 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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87 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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135 views

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 ...
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1answer
41 views

Detecting level in a Pulse Train

Assume I have a square wave pulse train, where each high lasts for H and each low lasts for L seconds. I sample this waveform and have the sequence of numbers. Question is what should be the sampling ...
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artifact identification in irregular-samped data

There is a dataset combined by different datasets a,b,c,d,e. The time intervals are irregular(i1, i2, i3:intervals between a and b, b and c...), but the sampling rate SR in every single dataset is the ...
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121 views

How do I extrapolate a 1D chirped signal?

Following a past question, I'd like to extrapolate a signal like the one below: (red is signal, blue is the the extrapolated ) ...
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1answer
377 views

Convert 96 Khz to 48 Khz audio: is this simple downsampling method ok?

I have an audio signal x sampled at 96 Khz. I have already lowpassed it with a cutoff somewhere between 20 Khz and 22 Khz, so there should be nothing left of ...
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1answer
392 views

Reconstruction of a signal from non-uniform samples [duplicate]

So I'm having some troubles with a signal that's been sampled but where the samples don't have consistent intervals. I've been looking into the NFFT (in python) as a starting point but I'm a complete ...
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1answer
999 views

MFCC window size at different sampling rates

The general recommendation for window size when calculating MFCC seems to be 20-40 msec. This is most often recommended in a context of 16000 samples per second, so leading to a window containing 320-...
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What kind of signal reppresents this Power Spectral Density?

I'm sampling 8 bioelectric signals with a embedded board which use an 8-channels ADC (AD7175-8). My sampling rate for every single channel is about 6250 Hz. When move the analysis in the frequency ...
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1answer
437 views

Bridging CTFT and DTFT for a cosine

I'm trying to understand how I can start from the CTFT of a signal and end up with a DTFT. For example if I take a basic example: $$\begin{aligned} x(t) &= \cos(\omega_x \cdot t) = \frac{1}{2} \...
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2answers
125 views

How do ADC/DACs deal with out of sync signals near Nyquist frequency?

Let's say a converter is sampling continuously at 48 kHz and the incoming waveform is a sine wave at 24 kHz... How does it faithfully recreate the waveform if the samples are taken at points that are ...
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1answer
557 views

sampling rate Matlab

I have a rather strange but i thin interesting question. The idea is to gain a better understanding of sampling rate vs frequency shifting when playing audio. The idea is a little experiment: ...
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1answer
107 views

Shannon theorem and zero padding

Sorry if I ask a basic question but I am a bit lost. I have a data set in frequential domain, I need to go to time domain to perform time-gating and then going back to frequencies. In order to do ...
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1answer
225 views

Determining sampling rate for signal reconstruction

I want to know how to determine the signal sampling rate required to reconstruct electrical signals whose frequency components are unknown, such as, for example, signals of charge/discharge voltage on ...
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1answer
172 views

How to delay an audio signal by 1 microsecond? [duplicate]

I have an audio signal sampled at 44100Hz. I want to delay this signal by 1 microsecond (and maybe even less) for a steganographic purpose. Now if I delay it one sample, the corresponding time delay ...

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