# Questions tagged [sampling]

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

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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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: ...
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 ...