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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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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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91 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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38 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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67 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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23 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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61 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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88 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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57 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
76 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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2answers
106 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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181 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
226 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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200 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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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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41 views

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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158 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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124 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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68 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
57 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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23 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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93 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
129 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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180 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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315 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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39 views

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
142 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: $$ x(t) = cos(\omega_x \cdot t) = \frac{1}{2} \cdot \left( e^{j\...
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2answers
79 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
276 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
69 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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168 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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99 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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98 views

How can I mimic this ADC for a given resolution, sampling rate and input with MATLAB or Python?

I'm quite new to the area so I need help to progress at some point. Basically I have a signed 16 bit ADC which means it maps -10V to +10V range to 16 bit. So the max voltage +10V is 2^15-1 = 32767; ...
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How can I extract the 2 polyphase components of a signal after sampling at the half of sampling rate

Suppose I have a continuous signal x(t), which was sampled using sampling function s(t) whose sampling rate is Ts.How can I sample the continuous signal by Ts/2 instead of Ts in order to get two ...
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Designing an experiment to show blue noise not adding noise below nyquist and not aliasing above

I read this paper from 1983 "Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina". This paper talks about blue noise sampling patterns in the retina and says that: The results (...
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Can we sample the signal with any period as long as the Nyquist rate is respected

I have a question regarding the sampling rate. Suppose that we transmitted a signal $m(t)$ then at receiver side, we received the continuous signal $x(t)$, which is time varying and sampled with a ...
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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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199 views

How can I show DTFT result in MATLAB? [closed]

I wanna show DTFT result and convolution result in f-domain are same. Additionally, I wanna show sampled function and inverse fourier transform result are same too. How can I show this? If I use ...
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1answer
121 views

About phase unwrapping

I am not too familiar with phase-related problems so I need some suggestions or corrections in a problem that might be an old but easy one. Here is my problem: given a complex signal: $$y(t) = e^{j\...
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2answers
76 views

Understanding the conditions for recovering a discrete time signal through sampling

So, we had a very brief introduction to the Nyquist-Shannon sampling theorem (the discrete time version). While discussing this, we have seen that multiplying a discrete time signal $x[n]$ by an ...
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1answer
36 views

Numerical error while implementing a periodic pulse signal

I'm trying to illustrate the principle of constructing a periodic signal using an elementary pattern. This is the code I use (python 2.7 + numpy + scipy.signal) : ...
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214 views

Relation between the DTFT and CTFT in sampling- sample period isn't as the impulse train period

I will quote an answer of Matt L. from this post (I didn't comment there because I can't) If you have a continuous-time signal $x(t)$, then the two signals you're talking about are $$\begin{...
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1answer
61 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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1answer
61 views

Is Oversampling a Signal Same as Discretizing the Signal?

I am confused about the new terminology 'oversampling' I have encountered very recently. To explain it better, I am going to use numerical examples. Now let's assume I am using a BPSK modulator and my ...
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88 views

How is a signal changed after sampling?

I can't understand sampling signal mathematically. for example $x(t) = 2\cos(100\pi t) + \cos(300\pi t)$ and I know I should use sampling frequency $300\textrm{Hz}$ to sample this signal. and after ...
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170 views

frequency spectrum of a sampled signal, PSD and power discussion

Before I go into my question, I first want to review the basics of sampling a signal and at the same time I build the basics of my questions so that they make more sense. I know I have asked couple of ...
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1answer
520 views

How Does the RMS of White Noise Change with Sampling Frequency?

There is an analog system which includes the continuous-time linear equalizer (CTLE). With some .noise analysis the power-spectral density (PSD) of the noise in that system is provided. So let's not ...
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70 views

Distortion of a signal consisting of two periodic components

We have a signal $$x(t)=U_1\cos\omega_1t+U_2\cos\omega_2t$$ whose frequencies are $f_1=100\,\text{Hz}$ and $f_2=600\,\text{Hz}$. This signal is being discretisated in time using unipolar ...